Advice 1: How to root number

The operation of raising a number to a power means finding the result of multiplying it by itself the number of times which is one less than specified in the exponent. However, not always the exponent is an integer - sometimes it is necessary, for example, to build a number to a power, which is represented by the expression containing the operation of root extraction.
How to root number
Start with calculation or conversion to a more convenient form of exponent, which includes the operation of root extraction. For example, if a task requires the number 25 to the extent that the measure which is the cubic root of the number 81, then "remove" it and replace the expression (3√81) obtained a value of (9).
If the resulting root extraction in the previous step, the number is a decimal, then try to submit it in the format of fractions. For example, if the conditions of the problem from the previous step, the exponent replaced by the cube root of the number of 3,375, the result of its calculation you will get a decimal of 1.5. It can be written in the format of an ordinary improper fraction 3/2. The construction of number 25 in such fractional degree means that it is necessary to remove the root of the second degree, as this number is in the denominator of the indicator, and raised to the third power, as this number is in the numerator (√253). Unfortunately not all decimal fraction can be represented in the form of fractions - often the result of the root extraction is an infinite fraction that is an irrational number.
Use the calculator as an indicator containing the extraction of roots, and the value of the whole expression. If you only want to get the result, omitting the intermediate transformations, it is possible to do only one Internet - easy-to-use calculator built in, for example, in the Google search engine. For example, if the required number of 3.87 to build in a degree which is equal to the square root of the number 62,7 then type in the search query box Google 3,87^sqrt(62,7). The result of the calculation (45049,6293), the search engine will show itself, even without pressing the button send query.

Advice 2: As you say " to the degree

The construction of the degree is one of the simplest algebraic operations. In everyday life the construction is rare, but on production, when you perform calculations – virtually everywhere, so it is useful to recall how this is done.
It is convenient to use a calculator
Suppose we have some number a, the degree of which is the number n. To build a number to a power means to multiply the number a to itself n times.
Consider a few examples.

To build the number 2 in the second degree, you must produce action:

To build the number 3 in the fifth degree, you must take action:

There is no generally accepted designation of the second and third degree numbers. The phrase "second degree" is usually replaced by the word "square" instead of the phrase "the third degree" usually say "cube".
As can be seen from the above examples, the duration and the complexity of calculations depends on the magnitude of the exponent of the number. Square or cube – a relatively easy task; raising a number to the fifth or greater degree already requires more time and accuracy in calculations. To accelerate this process and to avoid errors, you can use a special mathematical tables or a scientific calculator.

Advice 3: How to put in 1 degree

For a brief record of the works of one and the same number by itself, mathematicians have invented the concept of degree. Therefore, the expression 16*16*16*16*16 you can write the shorter way. It would be 16^5. The expression will be read as number 16 in the fifth degree.
How to put in 1 degree
You will need
  • Paper, pen.
In General, the degree is written as a^n. This entry means that the number a multiplied by itself n times.
The expression a^n is called the degree ofu,
a is the number of base degree,
n is a number, the exponent. For example, a = 4, n = 5,
Then write 4^5 = 4*4*4*4*4 = 1 024
The degree n can be a negative number
n = -1, -2, -3, etc.
To compute the negative degree numbers must be omitted in the denominator.
a^(-n) = (1/a)^n = 1/a*1/a*1/a* ... *1/a = 1/(a^n)
Consider the example
2^(-3) = (1/2)^3 = 1/2*1/2*1/2 = 1/(2^3) = 1/8 = 0,125
As can be seen from the example, -3 the degree of the number 2 can be calculated in different ways.
1) First calculate the fraction 1/2 = 0,5; and then to build in a degree of 3,
ie 0,5^3 = 0,5*0,5*0,5 = 0,125
2) First build in the denominator degree 2^3 = 2*2*2 = 8, and then calculate the fraction 1/8 = 0,125.
Now compute -1 degree for the number, i.e., n = -1. The rules discussed above are suitable for this case.
a^(-1) = (1/a)^1 = 1/(a^1) = 1/a
For example, let's build the number 5 to -1 degree
5^(-1) = (1/5)^1 = 1/(5^1) = 1/5 = 0,2.
From the example clearly shows that the number -1 is the inverse fraction of the number.
Imagine the number 5 as a fraction 5/1, then 5^(-1) arithmetically not take it and immediately write the inverse of 5/1 is 1/5.So, 15^(-1) = 1/15,
6^(-1) = 1/6,
25^(-1) = 1/25
When raising a number to a negative exponent, it should be remembered that the number can't be zero. According to the rule, we need to lower the number in the denominator. And zero cannot be the denominator, because zero cannot be split.
Useful advice
Sometimes when working with degrees for ease of calculation, the fractional number of specially replace the integer to -1 degree
1/6 = 6^(-1)
1/52 = 52^(-1).

Advice 4: How to build a root to a power

For a quick solution of examples it is necessary to know the properties of the roots and of the options available with them to perform. One of these intermediate task — the construction of the root in the degree. The result of the example is converted to a simpler, more accessible for the elementary calculations.
How to build a root to a power
Set the radical number a>=0, from which is extracted the root. Suppose for example a=8. Also referred to as the number standing under the root sign.
Write the integer n1. It is called the index of the root. If n=2, we are talking about the square root of a number. If n=3, the root is called cubic. For example, let us take n=6.
Select an integer k — the degreein which it is necessary to erect root. Let k=2.
Specify the resulting solution for example. In this case, you have to square root to the sixth power of the number eight.
To solve the problem erect in the degree of radical number: 82=64.
Formulate the resulting problem: now you need to extract the root of the sixth power of the number 64.
Convert radical expression: 64=8*8, i.e. it is necessary to extract the root of the sixth power of two multipliers. Otherwise can be written as: the root of the sixth power of eight multiplied by the root of the sixth power of the number eight. Another option the recording: the root of the sixth power of the number eight in the square.
Another transform used in the example: 6=3*2. Now square — number two — is in radical expression and exponent. Therefore, they can be mutually reduced, then an example will be, the root of the third degree of the number eight. Cubic root of eight equals two is the answer.
To build the root in the degree in another way, after the fourth step of the transform from n=6=3*2. Number two is in degree, and in the figure of the root, so the two can be reduced.
Write down the transformed problem: find the root of the third degree of the number eight. With the radicals did not have to do anything, because the sample is immediately simplified. The answer is two cubic root of eight.
Is the advice useful?