How to Find Negative Exponents in Algebra

Finding Negative Exponents in Algebra

A power with a negative exponent is equal to the reciprocal of the power (1 over the power) with the exponent made positive.

Imagine we have the letter a with an exponent of −n. We put the whole power under 1 and remove the minus sign from the exponent. This is equal to 1an.

a to the minus n equals 1 over 2 to the n

This is a laws of exponents.

How to Find Negative Exponents in Algebra

Question

Use the law of exponents to find the power with the negative exponent below.

x to the minus 2

Step-by-Step:

1

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

1 over the line

2

Write the power from the question on the bottom of the fraction (called the denominator).

1 over x to the minus 2

3

Remove the minus sign from the exponent. In our example, the exponent of −2 becomes 2.

1 over x to the 2

Answer:

We have found the negative exponent.

1 over x squared

Understanding Finding a Negative Exponent in Algebra

Let us look at the rule for negative exponents in algebra:

bases and exponents
  • a-−n and an are powers.

  • The bases of the powers are a.

  • The exponent of a−n is −n and the exponent of an is n.

  • The fraction 1an is the reciprocal of an.

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The slider below shows another real example of how to find negative exponents.

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See Also

What is algebra? The laws of exponents What is an exponent? What is a negative number? The laws of exponents