## Negative Exponents

## Definitions

Exponents are also calledPowersorIndices

The exponent of a number says how many times to use the number in a multiplication.

Example

7^{2} = 7 × 7 = 49

7^{2} can be called **7 to the second power** or **7 to the power 2** or simply **7 squared**

## General form of exponent

*a** ^{n}* tells you to use

*a*in a multiplication

*n*times

Those are positive exponents

## How About Negative Exponents?

Dividing is the inverse (opposite) of Multiplying.

A negative exponent means how many times to divide by the number.

Example

2^{-1} = 1 ÷ 2 = 1/2 = 0.5

many divides

2^{-2} = 1 ÷ 2 ÷ 2 = 0.25

Or

2^{-2} = 1 ÷ (2 × 2) = 1/2^{2} = 1/4 = 0.25

*a** ^{-n}* tells you to divide by

*a*

*n*times

## Easy Way

An easier way to handle negative exponents:

1. Calculate the positive exponent *a ^{n}*

2. Then take the Reciprocal 1/ *a ^{n}*