Rules of Exponents

Introduction Product Rule—when multiplying with the same base, add exponents. Quotient Rule—when dividing with the same base, subtract exponents. Power Rule—when raising a power to a power, multiply exponents.

Goal: Multiply Powers  To multiply powers with the same base, add their exponents.  a m a n = a m + n

Guided Practice Find the product. Write your answer using exponents.   = 4 18   = 2 17   = 5 11  x 6 x 13  x = x 19  b 2 b 4 b  b = b 7  2x 2 7x 6  2 7 x  14x 8

Independent Practice Find the product. Write your answer using exponents n 8 n 9 5. y 10 y (-a) 8 (-a) d 4 d h 5 4h g 2 g 16

Goal: Divide Powers  To divide powers with the same base, subtract their exponents.  a m = a m - n a n

Guided Practice Find the quotient. Write your answer using exponents.   4 11 – 7 = 4 4   2 12 – 5 = 2 7  x 9  x 3  x 9 – 3 = x 6  x 13  x 3  x 13 – 3 = x 10  b 4 b  b 4 – 1 = b 3  35x 6 7x 2  35  7 x 6 –2  5x 4

Independent Practice Find the quotient. Write your answer using exponents x 9  x 3 4. x 13  x 3 5. y 20  y b 4 b 7. 49x 5 7x x 6 5x 9. 36x 8 9x 3

Goal: Raise a power to a power  To raise a power to a power, multiply their exponents.  (a m ) n = a m n

Guided Practice Find the power. Write your answer using exponents.  (4 7 ) 11  = 4 77  (2 5 ) 12  = 2 60  (5 6 ) 2  = 5 12  (x6)3 (x6)3 (x6)3 (x6)3  x 6 3 = x 18  (b 2 ) -4  b 2 -4 = b -8 =  1/b 8  (x -2 ) -3  x = x 6

Independent Practice Find the power. Write your answer using exponents. 1. (5 10 ) 2 2. (4 8 ) 3 3. (5 4 ) 3 4. (n 8 ) 2 5. (y 10 ) (a -5 ) (6 7 ) 8 8. (d 4 ) (h -5 ) (g 2 ) 16

Summary Product Rule—when multiplying with the same base, add exponents. Quotient Rule—when dividing with the same base, subtract exponents. Power Rule—when raising a power to a power, multiply exponents.