1. Essential Question: What is the first step for simplifying an exponential expression that contains negative exponents?

2. 1) Zero as an exponent  Any number to the 0 power equals 1  Why? ▪ x 3 = 1x 1x 1x ▪ x 7 = 1x 1x 1x 1x 1x 1x 1x ▪ x 0 = no “x”s, so we leave just a “1” 2) Negative exponents  Any number to a negative exponent moves the base to the opposite side of a fraction, and the exponent becomes positive

3.  Simplify: 4 -3  Negative exponent. Move the base.  Make the exponent positive.

4.  Simplifying Expressions  Simplify 4y 0 x -3  Exponent of 0 = 1 Move negative exponent Make exponent positive

5.  Y OUR T URN – Simplify each expression  3 -4  -7 0  11m -5 

6.  Multiplying Same Bases (add)  When two numbers are multiplied together and have the same base, their exponents are added.  Why? ▪ x 3 = x x x ▪ x 5 = x x x x x ▪ x 3 x 5 = x x x x x x x x = x 8 ▪ x 3 x 5 = x 3+5 = x 8

7.  Dividing Same Bases (subtract)  When two numbers are divided and have the same base, their exponents are subtracted.  Why? ▪ x 3 = x x x ▪ x 5 = x x x x x ▪

8.  Power to a power (multiply)  If an exponent is raised to a power (typically outside a parenthesis), multiply the exponents together.  Examples: ▪ (3x 2 y 3 ) 4 = 3 4 x 8 y 12 = 81x 8 y 12 ▪

9.  Y OUR T URN – Simplify each expression  (7a 2 )(-2a -5 ) 

10.  Assignment  Page 368  1 – 24 (all)