The Lesson

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 1⁄2.

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.

Question

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

Step-by-Step:

1

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

3

2

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

1 over the line

3

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

1 over 3

Answer:

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

Lesson Slides

The slider below shows another real example of how to find an exponent of −1. Open the slider in a new tab

What Is a Reciprocal?

A reciprocal of a number is 1 divided by the number. reciprocals of numbers

Reciprocal of a Fraction

The reciprocal of a fraction just flips the fraction upside down. reciprocals of fractions