Aim: What are the product and power rules of exponents? Do Now: Simplify the following expressions 1. 𝑥∙𝑥 2. 𝑥∙ 𝑥 2 3. 𝑥∙𝑦

Product Rule for Exponents: 𝑥 𝑎 ∙ 𝑥 𝑏 = 𝑥 𝑎+𝑏 Power Rule for Exponents: 𝑥 𝑎 𝑏 = 𝑥 𝑎𝑏 1. 2x2 • 3x4 2. (2x2y)(7xy3z2) 3. (x3)2 4. (-5xy4z2)4

Find the product of each of the following monomials. 1. ( 5𝑥 2 )( 3𝑥 6 ) 2. −2𝑥 −6 𝑥 4 3. 3 2 𝑥 4 6𝑥 10 4. 3𝑥 4 −4 𝑥 4 2

5. 𝑥 2 𝑛 ∙ 𝑥 2 3 6. 2 𝑥 3 3 𝑥 5 6𝑥 2 If 𝑥=5 𝑎 4 ,and 𝑎=2 𝑏 3 , express 𝑥 𝑖𝑛 𝑡𝑒𝑟𝑚𝑠 𝑜𝑓 𝑏

Use the distributive property to multiply the following monomials and polynomials. 1. 2x(5x+3) 2. 5 𝑥 3 (2 𝑥 3 −3𝑥+6) 3. −7 𝑥 2 ( 𝑥 2 −2𝑥+3) 4. 3 𝑥 2 𝑦 4 (2 𝑥 2 𝑦+𝑥 𝑦 2 −4 𝑦 3 )