# Documentation/Calc Functions/POWER

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POWER

Mathematical

## Summary:

Raises one number (the base) to the power of another number (the exponent). This mathematical operation is known as exponentiation.

## Syntax:

POWER(Base; Exponent)

## Returns:

Returns a real number that is the specified base raised to the power of the given exponent.

## Arguments:

Base is a real number, or a reference to a cell containing that number, that is the base value.

Exponent is a real number, or a reference to a cell containing that number, that is the exponent value.

• If either Base or Exponent is non-numeric, then POWER reports a #VALUE! error.
• If Base is equal to 0 and Exponent is negative, then POWER reports a #NUM! error.
• If Base is negative and Exponent is non-integer, then POWER reports a #NUM! error.
• If both Exponent and Base are 0, then POWER returns 1.

• The formula for this function is $\displaystyle{ \text{POWER}(a; b)\:=\:a^b }$.
• POWER cannot be used with a negative base and a non-integer exponent. This means, for example, that you cannot use POWER to solve expressions such as $\displaystyle{ (-1)^{0.5} }$ – this is equivalent to $\displaystyle{ \sqrt{-1} }$ which has no real solution.
• Calc's exponentiation operator (^) produces the same result as that obtained from POWER. For example, the formula =2^3 gives the same result as =POWER(2; 3).
• For more background information about the exponentiation operator, visit Wikipedia’s Exponentiation page.

## Examples:

Formula Description Returns
=POWER(5; 3) Here the function raises 5 to the power of 3. This is equal to $\displaystyle{ 5\times5\times5 }$. 125
=POWER(D1; D2) where cells D1 and D2 contain the numbers 5.5 and 3.7 respectively. Here the function raises 5.5 to the power of 3.7. 548.708832614192
=POWER(2; −3) Here the function raises 2 to the power of -3. The value 2-3 is equal to $\displaystyle{ \frac{1}{2^3} }$ or $\displaystyle{ \frac{1}{8} }$. 0.125
=POWER(−5; 3) Here the function raises -5 to the power of 3. This is equal to $\displaystyle{ -5 \times -5 \times -5 }$. −125
=POWER(−3; −4) Here the function raises -3 to the power of -4. This is equal to $\displaystyle{ \frac{1}{(-3)^4} }$ or $\displaystyle{ \frac{1}{81} }$. 0.012345679012346

POWER