# Finding Negative Exponents

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 12n.

This is a laws of exponents.

# How to Find Negative Exponents

#### An Example Question

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

Step 1

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

Step 2

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

Step 3

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

We have used the law of exponents to express the power with a negative exponent as a power with a positive exponent.

As the final step, evaluate the power with the positive exponent.

Step 4

Evaluate the power on the bottom of the fraction. In our example, evaluate 32.

32 = 3 × 3 = 9

3-2 is equal to 19.

# 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 12n is the reciprocal of 2n.

# Real Example of How to Find Negative Exponents

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

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# 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.