The calculator below can solve for either the final value of a variable x raised to an exponent n, or it can calculate an exponent n, given a variable X and a final value y.

## Exponents Formula

X^{n} = Y

## What are exponents?

An exponent is a term used in algebra to describe the factoring number in the algebraic equation shown above. Factoring is the process of multiplying a number by itself some number of times. For example, 2 raised to a factor of 2 (2^{2}) is equal to 2 * 2 = 4. Another example is 3 raised to a factor of 4, which is equal to 3^{4} = 3*3*3*3 = 81. In these problems, the factor the original number is raised to is often referred to as the exponent n.

## How to calculate an exponent?

The following example is similar to the ones described in the section above. This example will follow the calculation given the variable x and exponent n.

- The fist step is to determine the values of both X and n. In this case, we will assume x=5 and n=3.
- The next step is to set up the factor equation to solve for Y. This equation should look like the following, 5
^{3}= Y. - The final step is to multiply 5 by itself 3 times, so 5*5*5 = 125.

This next example will show you how to calculate the exponent given the original variable X and the final value Y.

- In this example let’s assume X = 8 and Y = 64.
- The first step is to understand that a logarithm is the inverse of an exponent. Therefore, the exponent can be calculated using the log of Y with a base of X.
- Finally solve the equation of n = log8(64)= 2.

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