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Why are degrees needed? Where will you need them? Why should you take the time to study them?

To learn everything about degrees, what they are for, how to use your knowledge in everyday life read this article.

And, of course, knowledge of degrees will bring you closer to success passing the OGE or the Unified State Exam and admission to the university of your dreams.

Let's go... (Let's go!)

ENTRY LEVEL

Raising to a power is the same mathematical operation like addition, subtraction, multiplication or division.

Now I'll explain everything human language very simple examples. Be careful. The examples are elementary, but explain important things.

Let's start with addition.

There is nothing to explain here. You already know everything: there are eight of us. Everyone has two bottles of cola. How much cola is there? That's right - 16 bottles.

Now multiplication.

The same example with cola can be written differently: . Mathematicians are cunning and lazy people. They first notice some patterns, and then figure out a way to “count” them faster. In our case, they noticed that each of the eight people had the same number of cola bottles and came up with a technique called multiplication. Agree, it is considered easier and faster than.

So, to count faster, easier and without errors, you just need to remember multiplication table. Of course, you can do everything slower, more difficult and with mistakes! But…

Here is the multiplication table. Repeat.

And another, more beautiful one:

What other clever counting tricks have lazy mathematicians come up with? Right - raising a number to a power.

Raising a number to a power

If you need to multiply a number by itself five times, then mathematicians say that you need to raise that number to the fifth power. For example, . Mathematicians remember that two to the fifth power is... And they solve such problems in their heads - faster, easier and without mistakes.

All you need to do is remember what is highlighted in color in the table of powers of numbers. Believe me, this will make your life a lot easier.

By the way, why is it called the second degree? square numbers, and the third - cube? What does it mean? Very good question. Now you will have both squares and cubes.

Real life example #1

Let's start with the square or the second power of the number.

Imagine a square pool measuring one meter by one meter. The pool is at your dacha. It's hot and I really want to swim. But... the pool has no bottom! You need to cover the bottom of the pool with tiles. How many tiles do you need? In order to determine this, you need to know the bottom area of ​​the pool.

You can simply calculate by pointing your finger that the bottom of the pool consists of meter by meter cubes. If you have tiles one meter by one meter, you will need pieces. It's easy... But where have you seen such tiles? The tile will most likely be cm by cm. And then you will be tortured by “counting with your finger.” Then you have to multiply. So, on one side of the bottom of the pool we will fit tiles (pieces) and on the other, too, tiles. Multiply by and you get tiles ().

Did you notice that to determine the area of ​​the pool bottom we multiplied the same number by itself? What does it mean? Since we are multiplying the same number, we can use the “exponentiation” technique. (Of course, when you only have two numbers, you still need to multiply them or raise them to a power. But if you have a lot of them, then raising them to a power is much easier and there are also fewer errors in calculations. For the Unified State Exam, this is very important).
So, thirty to the second power will be (). Or we can say that thirty squared will be. In other words, the second power of a number can always be represented as a square. And vice versa, if you see a square, it is ALWAYS the second power of some number. A square is an image of the second power of a number.

Real life example #2

Here's a task for you: count how many squares there are on the chessboard using the square of the number... On one side of the cells and on the other too. To calculate their number, you need to multiply eight by eight or... if you notice that a chessboard is a square with a side, then you can square eight. You will get cells. () So?

Real life example #3

Now the cube or the third power of a number. The same pool. But now you need to find out how much water will have to be poured into this pool. You need to calculate the volume. (Volumes and liquids, by the way, are measured in cubic meters. Unexpected, right?) Draw a pool: a bottom measuring a meter and a depth of a meter and try to count how many cubes measuring a meter by a meter will fit into your pool.

Just point your finger and count! One, two, three, four...twenty-two, twenty-three...How many did you get? Not lost? Is it difficult to count with your finger? That's it! Take an example from mathematicians. They are lazy, so they noticed that in order to calculate the volume of the pool, you need to multiply its length, width and height by each other. In our case, the volume of the pool will be equal to cubes...It's easier isn't it?

Now imagine how lazy and cunning mathematicians are if they simplified this too. We reduced everything to one action. They noticed that the length, width and height are equal and that the same number is multiplied by itself... What does this mean? This means you can take advantage of the degree. So, what you once counted with your finger, they do in one action: three cubed is equal. It is written like this: .

All that remains is remember the table of degrees. Unless, of course, you are as lazy and cunning as mathematicians. If you like to work hard and make mistakes, you can continue to count with your finger.

Well, to finally convince you that degrees were invented by quitters and cunning people to solve their own life problems, and not to create problems for you, here are a couple more examples from life.

Real life example #4

You have a million rubles. At the beginning of each year, for every million you make, you make another million. That is, every million of yours doubles at the beginning of each year. How much money will you have in years? If you are sitting now and “counting with your finger,” then you are a very hardworking person and... stupid. But most likely you will give an answer in a couple of seconds, because you are smart! So, in the first year - two multiplied by two... in the second year - what happened, by two more, in the third year... Stop! You noticed that the number is multiplied by itself times. So two to the fifth power is a million! Now imagine that you have a competition and the one who can count the fastest will get these millions... It’s worth remembering the powers of numbers, don’t you think?

Real life example #5

You have a million. At the beginning of each year, you earn two more for every million. Great isn't it? Every million is tripled. How much money will you have in a year? Let's count. The first year - multiply by, then the result by another... It’s already boring, because you already understood everything: three is multiplied by itself times. So to the fourth power it is equal to a million. You just have to remember that three to the fourth power is or.

Now you know that by raising a number to a power you will make your life a lot easier. Let's take a further look at what you can do with degrees and what you need to know about them.

Terms and concepts... so as not to get confused

So, first, let's define the concepts. Do you think what is an exponent? It's very simple - it's the number that is "at the top" of the power of the number. Not scientific, but clear and easy to remember...

Well, at the same time, what such a degree basis? Even simpler - this is the number that is located below, at the base.

Here's a drawing for good measure.

Well in general view, in order to generalize and better remember... A degree with a base “ ” and an exponent “ ” is read as “to the degree” and is written as follows:

Power of number c natural indicator

You probably already guessed: because the exponent is natural number. Yes, but what is it natural number? Elementary! Natural numbers are those numbers that are used in counting when listing objects: one, two, three... When we count objects, we do not say: “minus five,” “minus six,” “minus seven.” We also do not say: “one third”, or “zero point five”. These are not natural numbers. What numbers do you think these are?

Numbers like “minus five”, “minus six”, “minus seven” refer to whole numbers. In general, integers include all natural numbers, numbers opposite to natural numbers (that is, taken with a minus sign), and number. Zero is easy to understand - it is when there is nothing. What do negative (“minus”) numbers mean? But they were invented primarily to indicate debts: if you have a balance on your phone in rubles, this means that you owe the operator rubles.

All fractions are rational numbers. How did they arise, do you think? Very simple. Several thousand years ago, our ancestors discovered that they lacked natural numbers to measure length, weight, area, etc. And they came up with rational numbers... Interesting, isn't it?

There are more irrational numbers. What are these numbers? In short, endless decimal. For example, if you divide the circumference of a circle by its diameter, you get an irrational number.

Resume:

Let us define the concept of a degree whose exponent is a natural number (i.e., integer and positive).

1. Any number to the first power is equal to itself:
2. To square a number means to multiply it by itself:
3. To cube a number means to multiply it by itself three times:

Definition. Raise the number to natural degree- means multiplying a number by itself times:
.

Properties of degrees

Where did these properties come from? I'll show you now.

Let's see: what is it And ?

By definition:

How many multipliers are there in total?

It’s very simple: we added multipliers to the factors, and the result is multipliers.

But by definition, this is a power of a number with an exponent, that is: , which is what needed to be proven.

Example: Simplify the expression.

Solution:

Example: Simplify the expression.

Solution: It is important to note that in our rule Necessarily must be identical grounds!
Therefore, we combine the powers with the base, but it remains a separate factor:

only for the product of powers!

Under no circumstances can you write that.

2. that's it th power of a number

Just as with the previous property, let us turn to the definition of degree:

It turns out that the expression is multiplied by itself times, that is, according to the definition, this is the th power of the number:

In essence, this can be called “taking the indicator out of brackets.” But you can never do this in total:

Let's remember the abbreviated multiplication formulas: how many times did we want to write?

But this is not true, after all.

Power with negative base

Up to this point, we have only discussed what the exponent should be.

But what should be the basis?

In powers of natural indicator the basis may be any number. Indeed, we can multiply any numbers by each other, be they positive, negative, or even.

Let's think about which signs ("" or "") will have powers of positive and negative numbers?

For example, is the number positive or negative? A? ? With the first one, everything is clear: no matter how many positive numbers we multiply by each other, the result will be positive.

But the negative ones are a little more interesting. We remember the simple rule from 6th grade: “minus for minus gives a plus.” That is, or. But if we multiply by, it works.

Determine for yourself what sign the following expressions will have:

Did you manage?

Here are the answers: In the first four examples, I hope everything is clear? We simply look at the base and exponent and apply the appropriate rule.

In example 5) everything is also not as scary as it seems: after all, it doesn’t matter what the base is equal to - the degree is even, which means the result will always be positive.

Well, except when the base is zero. The base is not equal, is it? Obviously not, since (because).

Example 6) is no longer so simple!

6 examples to practice

Analysis of the solution 6 examples

Whole we call the natural numbers, their opposites (that is, taken with the " " sign) and the number.

whole positive number , and it is no different from natural, then everything looks exactly like in the previous section.

Now let's look at new cases. Let's start with an indicator equal to.

Any number to the zero power is equal to one:

As always, let us ask ourselves: why is this so?

Let's consider some degree with a base. Take, for example, and multiply by:

So, we multiplied the number by, and we got the same thing as it was - . What number should you multiply by so that nothing changes? That's right, on. Means.

We can do the same with an arbitrary number:

Let's repeat the rule:

Any number to the zero power is equal to one.

But there are exceptions to many rules. And here it is also there - this is a number (as a base).

On the one hand, it must be equal to any degree - no matter how much you multiply zero by itself, you will still get zero, this is clear. But on the other hand, like any number to the zero power, it must be equal. So how much of this is true? The mathematicians decided not to get involved and refused to raise zero to the zero power. That is, now we cannot not only divide by zero, but also raise it to the zero power.

Let's move on. In addition to natural numbers and numbers, integers also include negative numbers. To understand what it is negative degree, let's do as in last time: multiply some normal number by the same number to a negative power:

From here it’s easy to express what you’re looking for:

Now let’s extend the resulting rule to an arbitrary degree:

So, let's formulate a rule:

A number to a negative power is the reciprocal of the same number to positive degree. But at the same time The base cannot be null:(because you can’t divide by).

Let's summarize:

Tasks for independent solution:

Well, as usual, examples for independent solutions:

Analysis of problems for independent solution:

I know, I know, the numbers are scary, but on the Unified State Exam you have to be prepared for anything! Solve these examples or analyze their solutions if you couldn’t solve them and you will learn to cope with them easily in the exam!

Let's continue to expand the range of numbers “suitable” as an exponent.

Now let's consider rational numbers. What numbers are called rational?

Answer: everything that can be represented as a fraction, where and are integers, and.

To understand what it is "fractional degree", consider the fraction:

Let's raise both sides of the equation to a power:

Now let's remember the rule about "degree to degree":

What number must be raised to a power to get?

This formulation is the definition of the root of the th degree.

Let me remind you: the root of the th power of a number () is a number that, when raised to a power, is equal to.

That is, the root of the th power is the inverse operation of raising to a power: .

It turns out that. Obviously this special case can be expanded: .

Now we add the numerator: what is it? The answer is easy to obtain using the power-to-power rule:

But can the base be any number? After all, the root cannot be extracted from all numbers.

None!

Let us remember the rule: any number raised to an even power is a positive number. That is, it is impossible to extract even roots from negative numbers!

This means that such numbers cannot be raised to fractional power with an even denominator, that is, the expression does not make sense.

What about the expression?

But here a problem arises.

The number can be represented in the form of other, reducible fractions, for example, or.

And it turns out that it exists, but does not exist, but these are just two different records of the same number.

Or another example: once, then you can write it down. But if we write down the indicator differently, we will get into trouble again: (that is, we got a completely different result!).

To avoid such paradoxes, we consider only positive base exponent with fractional exponent.

So if:

• — natural number;
• - integer;

Examples:

Degrees with rational indicator very useful for converting expressions with roots, for example:

5 examples to practice

Analysis of 5 examples for training

Well, now comes the hardest part. Now we'll figure it out degree with irrational exponent.

All the rules and properties of degrees here are exactly the same as for a degree with a rational exponent, with the exception

After all, by definition, irrational numbers are numbers that cannot be represented as a fraction, where and are integers (that is, irrational numbers are all real numbers except rational ones).

When studying degrees with natural, integer and rational exponents, each time we created a certain “image”, “analogy”, or description in more familiar terms.

For example, a degree with a natural exponent is a number multiplied by itself several times;

...number to the zeroth power- this is, as it were, a number multiplied by itself once, that is, they have not yet begun to multiply it, which means that the number itself has not even appeared yet - therefore the result is only a certain “blank number”, namely a number;

...degree with integer negative indicator - it’s as if some “reverse process” had occurred, that is, the number was not multiplied by itself, but divided.

By the way, in science a degree with a complex indicator is often used, that is, an indicator is not even real number.

But at school we don’t think about such difficulties; you will have the opportunity to comprehend these new concepts at the institute.

WHERE WE ARE SURE YOU WILL GO! (if you learn to solve such examples :))

For example:

Decide for yourself:

Analysis of solutions:

1. Let's start with the usual rule for raising a power to a power:

ADVANCED LEVEL

Determination of degree

A degree is an expression of the form: , where:

• — degree base;
• - exponent.

Degree with natural indicator (n = 1, 2, 3,...)

Raising a number to the natural power n means multiplying the number by itself times:

Degree with an integer exponent (0, ±1, ±2,...)

If the exponent is positive integer number:

Construction to the zero degree:

The expression is indefinite, because, on the one hand, to any degree is this, and on the other hand, any number to the th degree is this.

If the exponent is negative integer number:

(because you can’t divide by).

Once again about zeros: the expression is not defined in the case. If, then.

Examples:

Power with rational exponent

• — natural number;
• - integer;

Examples:

Properties of degrees

To make it easier to solve problems, let’s try to understand: where did these properties come from? Let's prove them.

Let's see: what is and?

By definition:

So, on the right side of this expression we get the following product:

But by definition it is a power of a number with an exponent, that is:

Q.E.D.

Example : Simplify the expression.

Solution : .

Example : Simplify the expression.

Solution : It is important to note that in our rule Necessarily there must be the same reasons. Therefore, we combine the powers with the base, but it remains a separate factor:

One more thing important note: this is the rule - only for product of powers!

Under no circumstances can you write that.

Just as with the previous property, let us turn to the definition of degree:

Let's regroup this work like this:

It turns out that the expression is multiplied by itself times, that is, according to the definition, this is the th power of the number:

In essence, this can be called “taking the indicator out of brackets.” But you can never do this in total: !

Let's remember the abbreviated multiplication formulas: how many times did we want to write? But this is not true, after all.

Power with a negative base.

Up to this point we have only discussed what it should be like indicator degrees. But what should be the basis? In powers of natural indicator the basis may be any number .

Indeed, we can multiply any numbers by each other, be they positive, negative, or even. Let's think about which signs ("" or "") will have powers of positive and negative numbers?

For example, is the number positive or negative? A? ?

With the first one, everything is clear: no matter how many positive numbers we multiply by each other, the result will be positive.

But the negative ones are a little more interesting. We remember the simple rule from 6th grade: “minus for minus gives a plus.” That is, or. But if we multiply by (), we get - .

And so on ad infinitum: with each subsequent multiplication the sign will change. We can formulate the following simple rules:

1. even degree, - number positive.
2. Negative number raised to odd degree, - number negative.
3. A positive number to any degree is a positive number.
4. Zero to any power is equal to zero.

Determine for yourself what sign the following expressions will have:

Did you manage? Here are the answers:

1) ; 2) ; 3) ; 4) ; 5) ; 6) .

In the first four examples, I hope everything is clear? We simply look at the base and exponent and apply the appropriate rule.

In example 5) everything is also not as scary as it seems: after all, it doesn’t matter what the base is equal to - the degree is even, which means the result will always be positive. Well, except when the base is zero. The base is not equal, is it? Obviously not, since (because).

Example 6) is no longer so simple. Here you need to find out which is less: or? If we remember that, it becomes clear that, and therefore the basis less than zero. That is, we apply rule 2: the result will be negative.

And again we use the definition of degree:

Everything is as usual - we write down the definition of degrees and divide them by each other, divide them into pairs and get:

Before you take it apart last rule, let's solve a few examples.

Calculate the expressions:

Solutions :

Let's go back to the example:

And again the formula:

So now the last rule:

How will we prove it? Of course, as usual: let’s expand on the concept of degree and simplify it:

Well, now let's open the brackets. How many letters are there in total? times by multipliers - what does this remind you of? This is nothing more than a definition of an operation multiplication: There were only multipliers there. That is, this, by definition, is a power of a number with an exponent:

Example:

Degree with irrational exponent

In addition to information about degrees for the average level, we will analyze the degree with an irrational exponent. All the rules and properties of degrees here are exactly the same as for a degree with a rational exponent, with the exception - after all, by definition, irrational numbers are numbers that cannot be represented as a fraction, where and are integers (that is, irrational numbers are all real numbers except rational numbers).

When studying degrees with natural, integer and rational exponents, each time we created a certain “image”, “analogy”, or description in more familiar terms. For example, a degree with a natural exponent is a number multiplied by itself several times; a number to the zero power is, as it were, a number multiplied by itself times, that is, they have not yet begun to multiply it, which means that the number itself has not even appeared yet - therefore the result is only a certain “blank number”, namely a number; a degree with an integer negative exponent - it’s as if some “reverse process” had occurred, that is, the number was not multiplied by itself, but divided.

It is extremely difficult to imagine a degree with an irrational exponent (just as it is difficult to imagine a 4-dimensional space). It is rather a purely mathematical object that mathematicians created to extend the concept of degree to the entire space of numbers.

By the way, in science a degree with a complex exponent is often used, that is, the exponent is not even a real number. But at school we don’t think about such difficulties; you will have the opportunity to comprehend these new concepts at the institute.

So what do we do if we see irrational indicator degrees? We are trying our best to get rid of it! :)

For example:

Decide for yourself:

Answers:

SUMMARY OF THE SECTION AND BASIC FORMULAS

Degree called an expression of the form: , where:

Degree with an integer exponent

a degree whose exponent is a natural number (i.e., integer and positive).

Power with rational exponent

degree, the exponent of which is negative and fractional numbers.

Degree with irrational exponent

a degree whose exponent is an infinite decimal fraction or root.

Properties of degrees

Features of degrees.

• Negative number raised to even degree, - number positive.
• Negative number raised to odd degree, - number negative.
• A positive number to any degree is a positive number.
• Zero is equal to any power.
• Any number to the zero power is equal.

NOW YOU HAVE THE WORD...

How do you like the article? Write below in the comments whether you liked it or not.

Tell us about your experience using degree properties.

Perhaps you have questions. Or suggestions.

Write in the comments.

And good luck on your exams!

Well, the topic is over. If you are reading these lines, it means you are very cool.

Because only 5% of people are able to master something on their own. And if you read to the end, then you are in this 5%!

Now the most important thing.

You have understood the theory on this topic. And, I repeat, this... this is just super! You are already better than the vast majority of your peers.

The problem is that this may not be enough...

For what?

For successful completion Unified State Exam, for admission to college on a budget and, MOST IMPORTANTLY, for life.

I won’t convince you of anything, I’ll just say one thing...

People who received good education, earn much more than those who did not receive it. This is statistics.

But this is not the main thing.

The main thing is that they are MORE HAPPY (there are such studies). Perhaps because there is much more open before them more possibilities and life becomes brighter? Don't know...

But think for yourself...

What does it take to be sure to be better than others on the Unified State Exam and ultimately be... happier?

GAIN YOUR HAND BY SOLVING PROBLEMS ON THIS TOPIC.

You won't be asked for theory during the exam.

You will need solve problems against time.

And, if you haven’t solved them (A LOT!), you’ll definitely make a stupid mistake somewhere or simply won’t have time.

It's like in sports - you need to repeat it many times to win for sure.

Find the collection wherever you want, necessarily with solutions, detailed analysis and decide, decide, decide!

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If you don't like our tasks, find others. Just don't stop at theory.

“Understood” and “I can solve” are completely different skills. You need both.

Find problems and solve them!

The calculator helps you quickly raise a number to a power online. The base of the degree can be any number (both integers and reals). The exponent can also be an integer or real, and can also be positive or negative. Please remember that for negative numbers, raising to a non-integer power is undefined and therefore the calculator will report an error if you attempt it.

Degree calculator

Raise to power

Exponentiations: 24601

What is a natural power of a number?

The number p is called the nth power of a number if p is equal to the number a multiplied by itself n times: p = a n = a·...·a
n - called exponent, and the number a is degree basis.

How to raise a number to a natural power?

To understand how to build different numbers to natural powers, consider a few examples:

Example 1. Raise the number three to the fourth power. That is, it is necessary to calculate 3 4
Solution: as mentioned above, 3 4 = 3·3·3·3 = 81.
Answer: 3 4 = 81 .

Example 2. Raise the number five to the fifth power. That is, it is necessary to calculate 5 5
Solution: similarly, 5 5 = 5·5·5·5·5 = 3125.
Answer: 5 5 = 3125 .

Thus, to raise a number to a natural power, you just need to multiply it by itself n times.

What is a negative power of a number?

In this case, a negative power exists only for non-zero numbers, since otherwise division by zero would occur.

How to raise a number to a negative integer power?

To raise a non-zero number to a negative power, you need to calculate the value of this number to the same positive power and divide one by the result.

Example 1. Raise the number two to the negative fourth power. That is, you need to calculate 2 -4

Answer: 2 -4 = 0.0625 .

Table of powers 2 (twos) from 0 to 32

The table below shows, in addition to powers of two, the maximum numbers that a computer can store for given number bit. Moreover, both for integers and signed numbers.

Historically, computers used the binary number system, and, accordingly, data storage. Thus, any number can be represented as a sequence of zeros and ones (bits of information). There are several ways to represent numbers as a binary sequence.

Let's consider the simplest of them - this is a positive integer. Then what larger number we need to write, the longer the sequence of bits we need.

Below is table of powers of number 2. It will give us a representation of the required number of bits that we need to store numbers.

How to use table of powers of number two?

The first column is power of two, which simultaneously denotes the number of bits that represent the number.

Second column - value twos to the appropriate power (n).

An example of finding the power of 2. We find the number 7 in the first column. We look along the line to the right and find the value two to the seventh power(2 7) is 128

Third column - the maximum number that can be represented using a given number of bits(in the first column).

An example of determining the maximum unsigned integer. Using the data from the previous example, we know that 2 7 = 128. This is true if we want to understand what number of numbers, can be represented using seven bits. But, since the first number is zero, then the maximum number that can be represented using seven bits is 128 - 1 = 127. This is the value of the third column.

Staphylococcus is considered an opportunistic microorganism. However, its excess amount is an indicator of the patient’s unfavorable health situation. In order to prevent infectious processes in a timely manner, examination for this bacterium is necessary.

What kind of microorganism is this?

This is the most common microorganism that humans encounter. There are many subspecies of bacteria - golden, epidermal and others. It lives on the skin, mucous membranes and in the human intestines. With developed local immunity and a normal balance of microflora, staphylococcus is not dangerous for the patient.

If there are any factors that weaken the immune system, or the patient faces a large number bacteria (most common example- food poisoning), and also damage to the mucous membrane occurs, inflammatory processes caused by staphylococcus occur.

An analysis for staphylococcus allows you to assess how great the risk of developing bacterial infections. Often the active growth of bacteria does not manifest itself in any way and has no external signs, and its presence can only be determined by laboratory methods.

Types of research

Since staphylococcus lives everywhere, there are a number of tests that can detect it. For each type there are certain rules collection of material and preparation. One of general rules– two weeks before the test you should not take antibiotics.

1. Blood test. Venous blood is required and is donated to medical institution. Indications: sepsis, suspicion of it, the presence of a large focus of infection in the body.
2. Examination of wound discharge. A smear is taken for analysis at a medical facility. Indications: the presence of a purulent wound.
3. Urine and stool examination. The patient collects the material independently; a sterile laboratory container is required. Sterility – important condition so that foreign microorganisms do not distort the result. Indications: genitourinary tract diseases and intestinal infections.
4. A swab from the mucous membranes, most often the nose or vagina. The material is collected by the doctor during the examination; this is a quick and painless procedure. Indications: infectious diseases of the ENT organs or genital tract in women.

Each of these tests confirms or denies the presence of bacterial overgrowth. An antibiotic sensitivity test can also be performed on the same material. In the presence of infectious diseases, it is done immediately, during a preventive examination - at the discretion of the doctor.

What should the norm be?

The normal result depends on the medium from which the smear is taken. Basically the rule is, the less the better.

• Blood and urine healthy person sterile, bacteria-free.
• The stool of a healthy patient contains a small amount of microorganisms - staphylococci are not the basis of the intestinal microflora. Positive result speaks of bacterial carriage or purulent disease.
• The presence of infection in the wound indicates a purulent infection or a high risk of its development.
• On mucous membranes, the upper limit of normal is considered to be 10*6 degrees - if there are more bacteria, this indicates the presence of a disease.

Selected indicators

The result is given as a number - this is the number of bacterial cells that have become the basis of the colony (CFU) per 1 ml of medium. The test is carried out on nutrient medium for bacteria - the material under study is placed in a special closed container, and if pathogens are present, they will begin to actively multiply.

The number of colonies arising from one sample of material is an indicator of the severity of the process. A growth of less than 10 colonies per sample is considered normal for mucous membranes and skin. From 10 to 100 colonies is an indicator of asymptomatic carriage of the pathogen. More than 100 colonies are a clear sign diseases.

10 to the 2nd power

• If such an indicator is found on the skin, nose or throat, this is variant of the norm. In this case, no action needs to be taken. If there are any problems with the skin, they are caused by other microorganisms.
• If such a concentration is found in feces, then feeling good it is considered the norm. Your doctor may be able to give you dietary recommendations. If there are symptoms of indigestion, the patient must begin treatment for dysbiosis.
• In the vagina, this result is typical for a smear with purity level 3 or 4. This does not mean disease, but predisposes to it. It is advisable to undergo vaginal sanitation, but this is not urgent. This result becomes dangerous only during pregnancy.
• In urine small quantity staphylococcus may indicate an inflammatory process or short-term bacteriuria. Repeated urine sampling is required after 2-3 days.
• Any number of microorganisms in the blood is a dangerous sign. If there are no symptoms of sepsis, a repeat test is required 2-3 days after receiving the results.
• The appearance of such a number of microorganisms in a wound is not an important diagnostic sign. Re-analysis required.

10 to 3

• This value is quite normal for the skin. The mucous membrane of the mouth and nose shows this result both normally and in cases of incipient diseases.
• Detection in feces is a possible carrier of the bacteria; repeated analysis is required.
• In the vagina the situation is similar to the previous point.
• In urine - most likely there is an inflammatory process in the urinary tract (urolithiasis, less commonly cystitis).
• In the wound there is a sign high risk development of purulent infection.

10 at 4

• Fixed on the skin for acne mild degree, but can be observed normally.
• The mucous membrane of the nose and pharynx is a sign of chronic respiratory infections.
• In the stool - bacteria carriage or dysbacteriosis; the patient is not recommended to work with food products or contact with children (sanitation is required), in other cases it is not necessary.
• In the vagina - indicator active growth pathogenic microflora.
• In urine it is characteristic of urolithiasis and cystitis in remission.
• In a wound - indicates that an infectious process has begun.

10 at 5

• On the skin - acne, furunculosis, can be observed in healthy people.
• Nasopharynx – chronic respiratory pathologies, colds with a risk of complications.
• Feces are carriers or an active infection.
• In the vagina - bacterial vaginitis.
• Urine – acute cystitis.

10 at 6

• On the skin - upper limit normal values, may occur with acne varying degrees expressiveness.
• In the nasopharynx - for infectious diseases.
• Other environments – acute inflammatory process.

Conclusion

Timely detection of the pathogen is necessary for the treatment and prevention of various health problems. First of all, this concerns the skin and mucous membranes, since it is there that pathogenic microflora is most often detected. You can fight it with antibiotics and agents that increase immunity (general and local). Also, do not forget about personal hygiene, proper nutrition and hardening.