Warm Up Simplify the expression.

7-2B Division Properties of Exponents RESTRICTION: Note: It is the variable that is restricted – not the exponent! Algebra 1 Glencoe McGraw-HillLinda Stamper For today’s problems assume that no denominator is equal to zero.

When working with division problems involving exponents, you can expand and cancel. You can cancel because any number or variable divided by itself is equal to one. / / 1 / / 1 / / 1 Can you expand and cancel this in your head? When you are expanding and canceling the exponents in your head, what mathematical operation are you using? Subtraction

When working with division problems involving exponents, you can expand and cancel. / / 1 / / 1 / / 1 / / 1 / / 1 Once you have practiced this, you may expand and cancel in your head! Here’s how…

Expand and cancel in your head! What is left and where is it located?

Example 1 Simplify. 1. Write problem. 2. Expand and cancel (you may do this in your head). What is left and where is it located (numerator or denominator)? 3. Simplify. You cannot cancel the base! Wrong answer! 1

Example 2 What is left and where is it located (numerator or denominator)? You cannot have a denominator without a numerator! Simplify. Example 3

A nonzero number to the zero power is 1. Zero to the zero power is undefined!

Example Simplify. Example 5 What is left and where is it located (numerator or denominator)? Example 6

Power of a Quotient Property To find a power of a quotient, find the power of the numerator and the power of the denominator and then divide. You must use parentheses!

Simplify. Example 7 Example 8 Must use parentheses! The exponent applies only to the base!

Simplify. Rewrite with positive exponents (powers with negative exponents need to be relocated) - keep the positive powers where they are given.

Simplify. Rewrite with positive exponents (powers with negative exponents need to be relocated) - keep the positive powers where they are given. Example 9 Example 10

Expressions Involving Fractions Rewrite with positive exponents - keep the positive powers where they are given. Multiply across the top (numerators) and across the bottom (denominators). What is left and where is it located? Expand and cancel.

Simplify. What is left and where is it located? Example 11 Rewrite with positive exponents (powers with negative exponents need to be relocated) - keep the positive powers where they are given. Example 12

7-A4 Page # 14–39,58-61,68.