Rules of Exponents

You can expand expressions to find their product. The following equation suggests a rule for multiplying powers with the same base when the exponents are integers.

Product of Powers Property 
To multiply powers with the same base, add their exponents.

Rule

Example

Using the Product of Powers Property

Example

Using the Product of Powers Property

Example

The following equation suggests a rule for dividing powers with the same base when the exponents are integers.

Quotient of Powers Property

To divide two powers with the same base, subtract the exponent of the denominator from the exponent of the numerator.

Rule

Example

Using the Quotient of Powers Property 

Simplify the expression. Write your answer as a power.

Example 1

Example 2

Practice

Simplify each expression.  Write your answer as a power.

1)  

2)  

Simplifying Fractions with Powers

Example 1

Example 2

Practice

Simplify the expression.  Write your answer as a power.

3)  

Complete each statement.

4)  Three is the _____________ of the expression 3⁴.

5)  Seven is the _____________ of the expression 4⁷.  

6)  Find and correct the error.  

2⁴  2² = (2  2)^{2 + 4}

                =  4⁶

7)   What is the value of 3² • 3² − 4³ ?

8)  What is another way to write the expression below?

9)  The table shows the number of meters in some metric measures. They are written as powers of ten.

How many kilometers are in a pentameter?

Answer Key