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to the power of

equals

The exponent calculator will calculate the value of any base raised to any power. This document will cover all the related topics, including the negative exponent. Let's start with the basics.

An exponent is a way to represent how many times a number, known as the base, is multiplied by itself. It is represented as a small number in the upper right hand corner of the base. For example: `x²`

means you multiply x times itself two times, which is `x * x`

. Likewise, `4² = 4 * 4`

, etc. If the exponent is 3, in the example `5³`

, then the result is `5 * 5 * 5`

.

It's easy with small numbers, but for bases that are large numbers, decimals, or when they are raised to the power that's a large or negative, use our tool. If you wish to do exponentiation by hand, do the following:

- Determine the base and the power it's raised to, for example
`3⁵`

. - Write the base the same number of times as the exponent.
`3 3 3 3 3`

- Place a multiplication symbol between each base.
`3 * 3 * 3 * 3 * 3`

. - Multiply!
`3 * 3 * 3 * 3 * 3 = 243`

.

The concept is rather simple when the it is positive, but what happens when the exponent is negative? By the definition, if it is -2, we would multiply the base times itself *negative two* times. In actuality, what is happening here, we take the reciprocal of the base and change the negative exponent to positive and proceed as usual. If you'd like to work it out by hand, do the following:

- Determine the base and the exponent.
- Write the reciprocal of the base and change the sign of the exponent to positive
- Write the reciprocal of the base the same number of times as the exponent.
- Place a multiplication symbol between each.
- Multiply and get the result.

Here's a quick example: `5⁻⁴ = (1/5)⁴ = (1/5) * (1/5) * (1/5) * (1/5) = 1/625 = 0.0016`

Squaring a base (raising to the power of 2) and taking the square root are similar concepts, many people consider one the opposite or the undoing of the other. If you want to square the number 6, you take `6 * 6 = 36`

. Now if you want to find what two identical numbers multiply to give you 36, you take the square root of 36. This square root gives the value of 6. It can also be noted that squaring a square root removes the radical. The square root calculator is an excellent tool that will calculate the square root of any positive number.