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 number 2 with an exponent of -n. We put the whole power under 1 and remove the minus sign from the exponent. This is equal to 1⁄2n.
How to Find Negative Exponents
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.


4
Evaluate the power on the bottom of the fraction. In our example, evaluate 32.
32 = 3 × 3 = 9
Answer:
We have found the negative exponent.
Understanding Finding a Negative Exponent
Let us look at the rule for negative exponents:
- 2−n and 2n are powers.
- The bases of the powers are 2.
- The exponent of 2−n is −n and the exponent of 2n is n.
- The fraction 1⁄2n is the reciprocal of 2n.
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, 22 means that 2 is multiplied by itself 2 times:
22 = 2 × 2
What Is a Reciprocal?
A reciprocal of a quantity (such as a letter or power) is 1 divided by the quantity.