1. Objectives Find the power of a power. Find the power of a product. Page 377 – Laws of Exponents: Powers and Products

2. Glossary Terms Power-of-a-Power Property Power-of-a-Product Property 8.2 Laws of Exponents: Powers and Products

3. Rules and Properties Power-of-a-Power Property For all nonzero real numbers x and all integers m and n, (x m ) n = x mn. When you have a power raised to a power, multiply the exponents.

4. Simplify and find the value of each expression if possible. (2³) 4 = 2 3·4 = 2 12 = 4096 (10³)² = 10 3·2 = 10 6 = 1,000,000 (p 2 ) 5 = P 2·5 = p 10 (x m ) 2 = x m·2 = x 2m

5. Rules and Properties Power-of-a-Product-Property For all real numbers, x and y, and all integers n, (xy) n = x n y n The exponent goes with everything inside the parentheses. It can be extended to include any number of factors inside the parentheses.

6. Simplify (x²y)³ =x 2·3 · y 1·3 =x6y3x6y3 (ab²c n ) 5 =a 1·5 · b 2·5 · c n·5 = a 6 b 10 c 5n

7. Rules and Properties Powers of –1 Even powers of –1 are equal to 1. Odd powers of –1 are equal to –1. 8.2 Laws of Exponents: Powers and Products

8. Simplify (-t) 5 =(-1·t) 5 = (-1) 5 · t 5 = -1 · t 5 =-t 5 -t 4 = This is already in simplest form. The exponent applies only to t. (-5x)³ = (-5)³ · x³ = -125x³

9. Key Skills Use the properties of exponents to simplify an expression. Simplify n 3 (2k 2 n 4 ) 2 Use the Power-of-a- Product Property. Use the Product-of- Powers Property. = n 3  4  k 4  n 8 = 4  k 4  n 3+8 = n 3  2 2  (k 2 ) 2 (n 4 ) 2 = n 3  4  k 2. 2  n 4. 2 8.2 Laws of Exponents: Powers and Products = 4k 4 n 11 Use the Power-of-a- Power Property. TOC

10. Assignment Page 381 #26 –52 even, 54 – 63