Unit 2 Lesson 4 Learn Properties of Exponents Power Rules

Basics (32)3 = (3  3) × (3  3) × (3  3) (32) (32) (32) = 36 Raising a power to a power is the same as raising the base to the product of the exponents.

For every nonzero number a and integers m and n, (am)n = amn When you raise a powers to a power, keep the base and multiply the exponents. Examples (44)2 = 48 (w2)5 = w10 (b0)7 = b0 = 1

Simplifying an Expression with Powers 1 310 32  (34) -3 = 32  3-12 = 3-10 =

Raising a Product to a Power (2x)4 = 24  x4 2x  2x  2x  2x = 16x4 For every nonzero number a and b and integer n, (ab)n = anbn

(3b)3 = 33  b3 = 27b3 (4ry)3 = 43  r3  y3 = 64r3y3 (2w2)4 = Examples (3b)3 = 33  b3 = 27b3 (4ry)3 = 43  r3  y3 = 64r3y3 (2w2)4 = 24  w8 = 16w8