# How to Simplify Exponents

In order to simplify exponents, you first have to know what an exponent is and how it's related to bases and powers

The base is the larger number that comes first. This is the number that you'll multiply by itself several times.

The exponent is the smaller number in the top right hand corner. The exponent tells you how many times you'll multiply the base by itself.

The combination of an exponent and a base is called a power

## How to Simplify Exponents

If the exponent is positive, you can follow these steps to simplify exponents:

1. Identify which number is the base and write down that number.
2. Identify which number is the exponent but do NOT write it down. Instead, write the base that number of times.
3. Multiply the repeated bases to find the simplified answer.

### Examples

$$9^{2}=9\times9=81$$

$$5^{4}=5\times5\times5\times5=625$$

$$100^{7}=100\times100\times100\times100\times100\times100\times100=$$

$$100000000000000$$

Check out these other pages to see how to simplify exponents if the exponent is a negative number, a fraction, 0, or 1

Negative

Exponent

Fraction

Exponent

Exponent

of Zero

Exponent

of One

Check out these pages to see how to simplify exponents if the base is a negative number, a fraction, a complex number or a polynomial

Negative

Base

Fraction

Base

Complex

Number

Polynomial

Base

## Exponents are Repeated Multiplication

In elementary school, you learned that multiplication makes repeated addition easier.

For example...

$$6\times4=6+6+6+6$$

$$3\times7=3+3+3+3+3+3+3$$

And repeated multiplication created exponents.

$$8^3=8\times8\times8$$

$$4^5=4\times4\times4\times4\times4$$

This relationship between addition, multiplication, and exponents is part of the structure that created the order of operations

## A Common Mistake

It's important to remember that an exponent means repeated multiplication, NOT regular multiplication.

A lot people make this common mistake when they first start learning about exponents...

### ExponentMistake

$$8^{4} \neq 32$$

$$8^{4} = 8\times 8\times 8\times 8 = 4,096$$

This mistake is very similar to another common mistake people make when they first learn multiplication...

### Multiplication Mistake

$$7 \times 3 \neq 10$$

$$7 \times 3 = 7+7+7=21$$

If you've made a mistake while simplifying exponents, don't worry :)

As you practice, it will become easier and easier and you'll soon be simplifying exponents as smoothly as you do multiplication now.