# Exponent Calculator

Enter the base and exponent to calculate the result below.

a^{x} = ?

## Results:

^{x}=

## How to Calculate an Exponent

An exponent is the number of times the base value should be multiplied by itself. To calculate a number raised to an exponent, multiply the number by itself for each value of the exponent.

So 5^{2} is the same as 5 × 5 and 5^{3} is the same as 5 × 5 × 5.

Calculating an exponent is also sometimes referred to as raising a number to the nth power.

**For example,** calculate the result of 8^{4}.

8^{4} = 8 × 8 × 8 × 8

8^{4} = 4,096

Thus, 8^{4}, or 8 to the 4th power, is equal to 8 times 8 times 8 times 8, which is equal to 4,096.

## How to Calculate a Negative Exponent

What do you do if the exponent is negative? For a negative exponent rather than multiplying the number by itself the number of times for the exponent, you divide the number by itself, starting with 1.

So 5^{-2} is the same as 1 ÷ 5 ÷ 5 and 5^{-3} is the same as 1 ÷5 ÷ 5 ÷ 5.

Negative exponents are often expressed as 1 over the base with a positive exponent.

5^{-2} = 15^{2}

**For example,** calculate the result of 8^{4}.

8^{-4} = 18^{4}

8^{-4} = 18 × 8 × 8 × 8

8^{-4} = 14,096

8^{-4} = 0.000244140625

Thus, 8^{-4} is equal to 0.000244140625.

## Special Exponent Rules

There are some special rules with exponents that are important to remember.

When the exponent is 1, the result of raising a base to the exponent will always be equal to the base.

a^{1} = a

When the exponent is 0, the result of raising a base to the exponent will always be equal to 1.

a^{0} = 1

When the exponent is 2 you can also say that the base value is squared. When the exponent is 3 you can say that the base value is cubed.

The calculator above will handle these special cases along with negative exponents to solve the answer.