How to use the POWER function
What is the POWER function?
The POWER function calculates a number raised to a power. You can also use the ^ character to perform a exponentiation in an Excel formula.
What is exponentiation?
Exponentiation is a mathematical operation involving exponents. It means raising a number, known as the base, to a specified power. The exponent indicates how many times to multiply the base by itself.
baseexponent
Roots are the inverse operation, giving the base when the power and number are known. For example,
x5 = 3125
3125(1/5) = 5
x = 5
55 = 3125
This makes it possible to calculate roots using the POWER function, however, to calculate square roots you can also use the SQRT function.
How are roots and logarithms related?
Roots and logarithms are inverse mathematical operations:
A root "undoes" exponentiation, finding the base number when given the power and result.
For example, √16 = 4, since 42 = 16. The root reveals the base of 4. √16 = 16(1/2)
A logarithm is the inverse of exponentiation as well, returning the exponent that a base must be raised to in order to produce a number.
For example, =log(8,2) = 3, since 23 = 8. The logarithm returns the exponent 3.
Logarithms calculate the exponent and roots calculate the base. This example demonstrates how to calculate the exponent:
5x = 3125
LOG5(3125) = 5
x = 5
55 = 3125
What are the other logarithmic functions in Excel?
| Excel function | Description |
|---|---|
| LOG | Returns the logarithm with a given base. |
| LN | Returns the natural logarithm (base e) of a number |
| LOG10 | Returns the base-10 logarithm of a number |
The corresponding inverse functions for the logarithm functions in Excel:
| Logarithm | Power to |
|---|---|
| LOG | Arbitrary base, basex or POWER(number, power) |
| LN | EXP(number) |
| LOG10 | 10x or POWER(10,x) |
What are the exponentiation rules?
Product Rule: xm * xn = x(m+n)
Exponents with the same base are multiplied when multiplying terms.
Power Rule: (xm)n = x(m*n)
When raising a power to a power, the exponents are multiplied.
Power of a Product: (ab)n = an * bn
Exponents distribute to all factors in a product.
Quotient Rule: xm / xn = x(m-n)
Exponents with the same base subtract when dividing terms.
Power of Quotient: (a/b)n = an / bn
Exponents distribute to the numerator and denominator when raising a quotient.
Any base raised to the 0 power equals 1.
Negative Exponent Rule: x-n = 1 / xn
Excel Function Syntax
POWER(number, power)
Arguments
| number | Required. The number you want to raise. |
| power | Required. The exponent to which the number is raised. |
Comments
The ^ operator is easier to use, example 10^2 = 100, number^power.
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Functions in 'Math and trigonometry' category
The POWER function function is one of 73 functions in the 'Math and trigonometry' category.
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