The Lesson
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 1⁄an.
How to Find Negative Exponents in Algebra
Question
Use the law of exponents to find the power with the negative exponent below.
Step-by-Step:
2
Write the power from the question on the bottom of the fraction (called the denominator).

3
Remove the minus sign from the exponent. In our example, the exponent of −2 becomes 2.

Answer:
We have found the negative exponent.
Understanding Finding a Negative Exponent in Algebra
Let us look at the rule for negative exponents in algebra:
- 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 1⁄an is the reciprocal of an.
What Is an Exponent?
An exponent tells you how many times a number or letter is multiplied by itself. An exponent is denoted by a raised number by the right hand side of the number (called the base) that is multiplied by itself. For example, a2 means that a is multiplied by itself 2 times:
a2 = a × a
What Is a Reciprocal?
A reciprocal of a quantity (such as a letter or power) is 1 divided by the quantity.
Reciprocals with Coefficients
What if there is a number or other letter written in front of a power with a negative exponent?
