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20161026 Power to Power and zero exponent 2.notebook Today is Wednesday 10/26 Do Now: Take out HW Put phone on notecard Copy down HW from side board -power to power w.s. *exponent quiz Friday Warm Up Express the following in exponential from: 6 multiplied times itself m times. a • a • a • a • ... • a (14 factors) What value of x makes the sentence true? 3 2 Simplify: x4 x7 x 3 8 = 3 8 y 3 y October 26, 2016 20161026 Power to Power and zero exponent 2.notebook October 26, 2016 20161026 Power to Power and zero exponent 2.notebook October 26, 2016 Today's Objective: Raising a Power to a Power Exponents to the Zero Power What is the following in simplest form? 2 3 (3 ) Write it in expanded form (3 x 3 )......3 times How many times do we use 3 as a factor? 20161026 Power to Power and zero exponent 2.notebook October 26, 2016 2 3 So.....to simplify (3 ) we get 3 6 3 4 What about (x ) Write it in expanded form How many times do we use x as a factor? 20161026 Power to Power and zero exponent 2.notebook October 26, 2016 So.....(x3)4 simplified is x12 What is happening???? Raising a power to a power Rule: When you raise a power to a power For any number x and positive integers a and b a b (x ) = ab x (52)6 = 5 2 x 6 = 512 20161026 Power to Power and zero exponent 2.notebook October 26, 2016 Exercise 1 (x2)0 (15 ) 3 2 (-16)7 Exercise 2 Sara wrote that (35)7 = 312. Why is she incorrect? Can you write an equation with a base of 3 , using exponents 5, 7 and 12 that would be true? 20161026 Power to Power and zero exponent 2.notebook October 26, 2016 What about (3 x 4)3 Write in simplest form 33 x 43 Exercise 3 (2 x 3)7 2 4 2 (qr s ) (5x) 7 2 3 7 (x y ) 20161026 Power to Power and zero exponent 2.notebook October 26, 2016 These are from tonight's HW! 4 4 3 (4x x ) 4 2 (6yx ) Exponents and fractions ( ) 1 2 2 3 ( ) 3 4 20161026 Power to Power and zero exponent 2.notebook October 26, 2016 Numbers raised to the Zero Power 4 4 500 = 500 = 4 5 4 = 5 Numbers raised to the Zero Power Rule: ANYTHING to the Zero Power is 1 50 = 1 20 = 1 (-5)0 = x0 = 20161026 Power to Power and zero exponent 2.notebook October 26, 2016