Ch 8: Exponents B) Zero & Negative Exponents Objective: To simplify expressions involving negative exponents and zero exponents.

Definitions Zero Exponent Any base (except 0) with an exponent of 0 equals 1 For example: x0 = 1, 20 = 1, 100 = 1, (5x)0 = 1 Negative Exponent Any base containing an exponent with a negative value should be “flipped” to change the exponent to a positive value. x−2 1 For example: = x2 1

Follow the Pattern! = 3 3 3 = 3 3 = 3 = 1 = = =

( ) ( ) Rules x x 2 2 2 Shortcuts apply to Negative Exponents = = = = Write expression in fraction format Draw a fraction bar Evaluate each base one at a time Positive exponents stay on the same side of the fraction bar Negative exponents move to the opposite side Shortcuts apply to Negative Exponents Power to Power Rule ( ) b ( ) -2 a 3 3(-2) -6 x x ab 2 2 2 = = = =

= = 16 = = = = = = = 3x2 1 1 42 1 31 4-1 51 3 x2 5-1 41 Example 1

= = = y2 z = = 7 x3 1 (5a)2 (5a) (5a) x y3 y2 z1 x3 7 Example 5

Classwork 1 1) 82 1 222 2) 55 1 222 3) 33 55 2-2 4) = 5-2 22

3 5) x2 6) 6 x y2 1 1 1 7) = = (6xy)2 (6xy)(6xy) 36 x2 y2 (2a-3) 2 4 8) = = a6b4 b4 a3 a3 b4