The Lesson

A letter with an exponent of −1 is equal to the reciprocal of the letter (1 divided by the letter). Imagine we have the letter a with an exponent of −1. This is equal to 1⁄a.

a to the minus 1 is equal to 1 over a This is a law of exponents.

How to Find an Exponent of −1 in Algebra

Finding an exponent of −1 in algebra 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 letter or symbol that has an exponent of −1. In our example, the letter is x.

x

2

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

1 over the line

3

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

1 over x

Answer:

We have found an exponent of −1.

x to the minus 1 equals 1 over x

Understanding Finding an Exponent of −1 in Algebra

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

bases and exponents

Lesson Slides

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

What Is a Reciprocal?

A reciprocal of a letter is 1 divided by the letter. reciprocals of letters

Reciprocal of a Fraction

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

Reciprocals with Coefficients

What if there is a number or other letter written in front of a letter with an exponent of −1?

2 x to the minus 1 The number or letter in front is a coefficient that is multiplying what comes after it. It goes on top of the fraction instead of 1.

2 over x