Table of powers of numbers from 1 to 10. Online powers calculator. Interactive table and images of the table of degrees in high quality.
Degree calculator
Number
Degree
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With this calculator you can calculate the power of any natural number online. Enter the number, degree and click the “calculate” button.
Table of degrees from 1 to 10
| n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 n | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 2n | 2 | 4 | 8 | 16 | 32 | 64 | 128 | 256 | 512 | 1024 |
| 3n | 3 | 9 | 27 | 81 | 243 | 729 | 2187 | 6561 | 19683 | 59049 |
| 4n | 4 | 16 | 64 | 256 | 1024 | 4096 | 16384 | 65536 | 262144 | 1048576 |
| 5n | 5 | 25 | 125 | 625 | 3125 | 15625 | 78125 | 390625 | 1953125 | 9765625 |
| 6n | 6 | 36 | 216 | 1296 | 7776 | 46656 | 279936 | 1679616 | 10077696 | 60466176 |
| 7n | 7 | 49 | 343 | 2401 | 16807 | 117649 | 823543 | 5764801 | 40353607 | 282475249 |
| 8 n | 8 | 64 | 512 | 4096 | 32768 | 262144 | 2097152 | 16777216 | 134217728 | 1073741824 |
| 9n | 9 | 81 | 729 | 6561 | 59049 | 531441 | 4782969 | 43046721 | 387420489 | 3486784401 |
| 10n | 10 | 100 | 1000 | 10000 | 100000 | 1000000 | 10000000 | 100000000 | 1000000000 | 10000000000 |
Table of degrees from 1 to 10
|
1 1 = 1 1 2 = 1 1 3 = 1 1 4 = 1 1 5 = 1 1 6 = 1 1 7 = 1 1 8 = 1 1 9 = 1 1 10 = 1 |
2 1 = 2 2 2 = 4 2 3 = 8 2 4 = 16 2 5 = 32 2 6 = 64 2 7 = 128 2 8 = 256 2 9 = 512 2 10 = 1024 |
3 1 = 3 3 2 = 9 3 3 = 27 3 4 = 81 3 5 = 243 3 6 = 729 3 7 = 2187 3 8 = 6561 3 9 = 19683 3 10 = 59049 |
4 1 = 4 4 2 = 16 4 3 = 64 4 4 = 256 4 5 = 1024 4 6 = 4096 4 7 = 16384 4 8 = 65536 4 9 = 262144 4 10 = 1048576 |
5 1 = 5 5 2 = 25 5 3 = 125 5 4 = 625 5 5 = 3125 5 6 = 15625 5 7 = 78125 5 8 = 390625 5 9 = 1953125 5 10 = 9765625 |
|
6 1 = 6 6 2 = 36 6 3 = 216 6 4 = 1296 6 5 = 7776 6 6 = 46656 6 7 = 279936 6 8 = 1679616 6 9 = 10077696 6 10 = 60466176 |
7 1 = 7 7 2 = 49 7 3 = 343 7 4 = 2401 7 5 = 16807 7 6 = 117649 7 7 = 823543 7 8 = 5764801 7 9 = 40353607 7 10 = 282475249 |
8 1 = 8 8 2 = 64 8 3 = 512 8 4 = 4096 8 5 = 32768 8 6 = 262144 8 7 = 2097152 8 8 = 16777216 8 9 = 134217728 8 10 = 1073741824 |
9 1 = 9 9 2 = 81 9 3 = 729 9 4 = 6561 9 5 = 59049 9 6 = 531441 9 7 = 4782969 9 8 = 43046721 9 9 = 387420489 9 10 = 3486784401 |
10 1 = 10 10 2 = 100 10 3 = 1000 10 4 = 10000 10 5 = 100000 10 6 = 1000000 10 7 = 10000000 10 8 = 100000000 10 9 = 1000000000 10 10 = 10000000000 |
Theory
Degree of is an abbreviated form of the operation of repeatedly multiplying a number by itself. The number itself in this case is called - degree basis, and the number of multiplication operations is exponent.
a n = a×a ... ×a
the entry reads: "a" to the power of "n".
"a" is the base of the degree
"n" - exponent
4 6 = 4 × 4 × 4 × 4 × 4 × 4 = 4096
This expression reads: 4 to the power of 6 or the sixth power of the number four or raise the number four to the sixth power.
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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. Keep in mind that for negative numbers, raising to a non-integer power is undefined, so the calculator will report an error if you attempt it.
Degree calculator
Raise to power
Exponentiations: 46086
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 raise various 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?
The negative power -n of a is one divided by a to the power of n: a -n = .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
Solution: as stated above, 2 -4 = = = 0.0625.Answer: 2 -4 = 0.0625 .
Enter the number and degree, then press =.
^Table of degrees
Example: 2 3 =8
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Properties of degree - 2 parts
A table of the main degrees in algebra in a compact form (picture, convenient for printing), on top of the number, on the side of the degree.
Continuing the conversation about the power of a number, it is logical to figure out how to find the value of the power. This process is called exponentiation. In this article we will study how exponentiation is performed, while we will touch on all possible exponents - natural, integer, rational and irrational. And according to tradition, we will consider in detail solutions to examples of raising numbers to various powers.
Page navigation.
What does "exponentiation" mean?
Let's start by explaining what is called exponentiation. Here is the relevant definition.
Definition.
Exponentiation- this is finding the value of the power of a number.
Thus, finding the value of the power of a number a with exponent r and raising the number a to the power r are the same thing. For example, if the task is “calculate the value of the power (0.5) 5,” then it can be reformulated as follows: “Raise the number 0.5 to the power 5.”
Now you can go directly to the rules by which exponentiation is performed.
Raising a number to a natural power
In practice, equality based on is usually applied in the form . That is, when raising a number a to a fractional power m/n, first the nth root of the number a is taken, after which the resulting result is raised to an integer power m.
Let's look at solutions to examples of raising to a fractional power.
Example.
Calculate the value of the degree.
Solution.
We will show two solutions.
First way. By definition of a degree with a fractional exponent. We calculate the value of the degree under the root sign, and then extract the cube root: 
.
Second way. By the definition of a degree with a fractional exponent and based on the properties of the roots, the following equalities are true: 
. Now we extract the root 
, finally, we raise it to an integer power 
.
Obviously, the obtained results of raising to a fractional power coincide.
Answer:
Note that a fractional exponent can be written as a decimal fraction or a mixed number, in these cases it should be replaced with the corresponding ordinary fraction, and then raised to a power.
Example.
Calculate (44.89) 2.5.
Solution.
Let's write the exponent in the form of an ordinary fraction (if necessary, see the article): 
. Now we perform the raising to a fractional power: 
Answer:
(44,89) 2,5 =13 501,25107 .
It should also be said that raising numbers to rational powers is a rather labor-intensive process (especially when the numerator and denominator of the fractional exponent contain sufficiently large numbers), which is usually carried out using computer technology.
To conclude this point, let us dwell on raising the number zero to a fractional power. We gave the following meaning to the fractional power of zero of the form: when we have 
, and at zero to the m/n power is not defined. So, zero to a fractional positive power is zero, for example, 
. And zero in a fractional negative power does not make sense, for example, the expressions 0 -4.3 do not make sense.
Raising to an irrational power
Sometimes it becomes necessary to find out the value of the power of a number with an irrational exponent. In this case, for practical purposes it is usually sufficient to obtain the value of the degree accurate to a certain sign. Let us immediately note that in practice this value is calculated using electronic computers, since raising it to an irrational power manually requires a large number of cumbersome calculations. But we will still describe in general terms the essence of the actions.
To obtain an approximate value of the power of a number a with an irrational exponent, some decimal approximation of the exponent is taken and the value of the power is calculated. This value is an approximate value of the power of the number a with an irrational exponent. The more accurate the decimal approximation of a number is taken initially, the more accurate the value of the degree will be obtained in the end.
As an example, let's calculate the approximate value of the power of 2 1.174367... . Let's take the following decimal approximation of the irrational exponent: . Now we raise 2 to the rational power 1.17 (we described the essence of this process in the previous paragraph), we get 2 1.17 ≈2.250116. Thus, 2 1,174367... ≈2 1,17 ≈2,250116 . If we take a more accurate decimal approximation of the irrational exponent, for example, then we obtain a more accurate value of the original exponent: 2 1,174367... ≈2 1,1743 ≈2,256833 .
Bibliography.
- Vilenkin N.Ya., Zhokhov V.I., Chesnokov A.S., Shvartsburd S.I. Mathematics textbook for 5th grade. educational institutions.
- Makarychev Yu.N., Mindyuk N.G., Neshkov K.I., Suvorova S.B. Algebra: textbook for 7th grade. educational institutions.
- Makarychev Yu.N., Mindyuk N.G., Neshkov K.I., Suvorova S.B. Algebra: textbook for 8th grade. educational institutions.
- Makarychev Yu.N., Mindyuk N.G., Neshkov K.I., Suvorova S.B. Algebra: textbook for 9th grade. educational institutions.
- Kolmogorov A.N., Abramov A.M., Dudnitsyn Yu.P. and others. Algebra and the beginnings of analysis: Textbook for grades 10 - 11 of general education institutions.
- Gusev V.A., Mordkovich A.G. Mathematics (a manual for those entering technical schools).
