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**.

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

- Identify which number is the base and write down that number.
- Identify which number is the exponent but do
__NOT__write it down. Instead, write the**base**that number of times. - Multiply the repeated bases to find the simplified answer.

\(9^{2}=9\times9=81\)

\(5^{4}=5\times5\times5\times5=625\)

\(100^{7}=100\times100\times100\times100\times100\times100\times100=\)

\(100000000000000\)

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

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.

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

For example...

\(6\times4=6+6+6+6\)

\(3\times7=3+3+3+3+3+3+3\)

Repeated addition created multiplication.

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.

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...

Mistake

\(8^{4} \neq 32\)

Answer

\(8^{4} = 8\times 8\times 8\times 8 = 4,096\)

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

Mistake

\(7 \times 3 \neq 10\)

Answer

\(7 \times 3 = 7+7+7=21\)

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.

Homeschool Math - Write Repeated Multiplication as Exponents

Homeschool Math - Whole Number Bases (Small)

Homeschool Math - Whole Number Bases (Bigger)

Homeschool Math - Fraction and Decimal Bases

The worksheets from Homeschool Math will generate new numbers every time you refresh the page. Answer keys are included.