How to Find an Exponent of −1

Finding an Exponent of −1

A number with an exponent of -1 is equal to the reciprocal of the number (1 divided by the number).

Imagine we have the number 2 with an exponent of -1. This is equal to 12.

2 to the minus 1 is equal to 1 over 2

This is a law of exponents.

How to Find an Exponent of −1

Finding an exponent of −1 is easy.


Use the law of exponents to find the power with an exponent of −1 below.

x to the minus 1



Find the number that has an exponent of −1. In our example, the number is 3.



Write 1 on the top of a fraction (called the numerator).

1 over the line


Write the letter from Step 1 (3) on the bottom of the fraction (called the denominator).

1 over 3


We have found an exponent of −1.

3 to the minus 1 equals 1 over 3

Understanding Finding an Exponent of −1

Let us look at the rule for an exponent of −1:

bases and exponents


The slider below shows another real example of how to find an exponent of −1.

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See Also

The laws of exponents What is a power? What is a base? What is an exponent? What is a reciprocal?