## 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.

base^{exponent}

Roots are the inverse operation, giving the base when the power and number are known. For example,

x^{5} = 3125

3125^{(1/5)} = 5

x = 5

5^{5} = 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, âˆš16 = 4, since 4^{2} = 16. The root reveals the base of 4. âˆš16 = 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 2^{3} = 8. The logarithm returns the exponent 3.

Logarithms calculate the exponent and roots calculate the base. This example demonstrates how to calculate the exponent:

5^{x} = 3125

LOG5(3125) = 5

x = 5

5^{5} = 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, base^{x}Â or POWER(number, power) |

LN | EXP(number) |

LOG10 | 10^{x}Â or POWER(10,x) |

**What are the exponentiation rules?**

Product Rule: x^{m} * x^{n} = x^{(m+n)}

Exponents with the same base are multiplied when multiplying terms.

Power Rule: (x^{m})^{n} = x^{(m*n)}

When raising a power to a power, the exponents are multiplied.

Power of a Product: (ab)^{n} = a^{n} * b^{n}

Exponents distribute to all factors in a product.

Quotient Rule: x^{m} / x^{n} = x^{(m-n)}

Exponents with the same base subtract when dividing terms.

Power of Quotient: (a/b)^{n} = a^{n} / b^{n}

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 / x^{n}

### Excel Function Syntax

POWER(*number, power*)

### Arguments

number |
Required. The number you want toÂ raise. |

power |
Required. The exponent to which the number is raised. |

### Comments

The ^ operator is easier to use, example 10^2 = 100, number^power.

### 'POWER' function examples

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### Functions in 'Math and trigonometry' category

The POWER function function is one of many functions in the 'Math and trigonometry' category.

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