Division Properties of Exponents “I can use the properties of exponents to simplify numerical expressions.” 8.M.EE.01

Review Simplify the following expressions: 3x・x2 (x2・y2)2 a2・a3・a5 2

Vocabulary Power Quotient Numerator Denominator 3

Quotient of Powers Property To divide powers having the same base, you subtract the exponents. Examples: 1) What is the base? 58-2 Subtract the exponents! 56 Simplify 15,625 Final Solution

Quotient of Powers Property To divide powers having the same base, you subtract the exponents. Examples: 2) What is the base? k9-5 Subtract the exponents! k4 Simplified Solution

Practice Simplify the following expressions:

Power of a Quotient Property To find a power of a quotient, find the power of both the numerator and the denominator and divide. The exponent outside the parentheses is “distributed” to everything inside the parentheses. Examples: 1) What is the numerator? What is the denominator? Distribute the power! Simplify and reduce.

( ) Power of a Quotient Property Examples: 2 2) What is the numerator? To find a power of a quotient, find the power of both the numerator and the denominator and divide. The exponent outside the parentheses is “distributed” to everything inside the parentheses. Examples: ( ) 2 2) What is the numerator? What is the denominator? Why 3x2? Distribute the power! Simplify and reduce.

Power of a Quotient Property Examples: 3) What is the numerator? What is the denominator? Distribute the power! Simplify and Reduce Simplified Solution!

Practice Simplify the following expressions:

Anything to the 0 power is equal to 1.

Practice Simplify the following expressions:

A negative exponent means you move the base to the other side of the fraction and make the exponent positive. Notice that the base with the negative exponent moved and became positive!

Negative Exponents - Examples Remember: You can not have negative or zero exponents in your answer!! 1) Simplify: Get rid of the negative exponent. Move to the bottom! Simplify Solution

Negative Exponents - Examples Remember: You can not have negative or zero exponents in your answer!! Get rid of the negative exponent!

Here’s a tricky one!

Practice Simplify the following expressions 17

Closure “We learned what?”