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

Click Here

Fraction

Exponent

Click Here

Exponent

of Zero

Click Here

Exponent

of One

Click Here

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

Click Here

Fraction

Base

Click Here

Complex

Number

Click Here

Polynomial

Base

Click Here

Exponents are Repeated Multiplication

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

For example...


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

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

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

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...

Exponent
Mistake

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

Correct
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...

Multiplication
Mistake

\(7 \times 3 \neq 10\)

Correct
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. 

Resources

Free Online Practice Problems

Khan Academy - Exponents (Basic)

Khan Academy - Exponents

Free Printable Worksheets

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.

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