Main Idea Key Concept Power of a Power

Main Idea Key Concept: Power of a Power Example 1: Find the Power of a Power Example 2: Find the Power of a Power Key Concept: Power of a Product Example 3: Power of a Product Example 4: Power of a Product Example 5: Real-World Example

• Use laws of exponents to find powers of monomials.

Find the Power of a Power Simplify (52)8 = 52 • 8 = 516 Answer: 516 Power of a Power Simplify.

Simplify (79)3. A. 73 B. 76 C. 712 D. 727

Find the Power of a Power Simplify (a 3)7 = a 3 • 7 = a 21 Answer: a 21 Power of a Power Simplify.

Simplify (d 5)5. A. d 25 B. d 5 C. d 1 D. d 0

Power of a Product Simplify (3 c 4)3 = 33 • c 4 • 3 = 27 c 12 Answer: 27 c 12 Power of a Product Simplify.

Simplify (8 r 7)2. A. 8 r 14 B. 16 r 14 C. 64 r 9 D. 64 r 14

Power of a Product Simplify (– 4 p 5 q)2 = (– 4)2 • p 5 • 2 • q 2 = 16 p 10 q 2 Answer: 16 p 10 q 2 Power of a Product Simplify.

Simplify (– 6 s 2 t 9)3. A. – 216 s 6 t 27 B. – 216 s 5 t 12 C. – 18 s 6 t 27 D. – 18 s 5 t 12

GEOMETRY Find the volume of a cube with side lengths of 6 mn 7. Express as a monomial. V = s 3 Volume of a cube V = (6 mn 7)3 Replace s with 6 mn 7. V = 63(m 1)3(n 7)3 Power of a Product V = 216 m 3 n 21 Simplify. Answer: The volume of the cube is 216 m 3 n 21 cubic units.

GEOMETRY Find the area of a square with side lengths of 5 q 8 r 5. Express as a monomial. A. 10 q 10 r 7 B. 10 q 16 r 10 C. 25 q 10 r 7 D. 25 q 16 r 10