Apply Properties of Rational Exponents Section 6-2 Day 1 Apply Properties of Rational Exponents

Properties of Radicals Product Property of Radicals 𝑛 𝑎∙𝑏 = 𝑛 𝑎 ∙ 𝑛 𝑏 Quotient Property of Radicals 𝑛 𝑎 𝑏 = 𝑛 𝑎 𝑛 𝑏 4 16𝑥 = 4 16 ∙ 4 𝑥 =2 4 𝑥

13 = 1 14 = 1 15 = 1 23 = 8 24 = 16 25 = 32 33 = 27 34 = 81 35 = 243 43 = 64 44 = 256 45 = 1024 53 = 125 54 = 625 55 = 3125 63 = 216 73 = 343 83 = 512

Example 1 Use the properties of rational exponents to simplify the expression. a.) 12 1 8 ∙ 12 5 6 = b.) ( 5 1 3 ∙ 7 1 4 ) 3 = c.) ( 2 6 ∙ 4 6 ) −1 6 = d.) 10 10 2 5 12 1 8 + 5 6 = 12 23 24 ( 5 1 3 ) 3 ∙ ( 7 1 4 ) 3 = 5∙ 7 3 4 ( 2 6 ) −1 6 ∙ ( 4 6 ) −1 6 = 2-1 • 4-1 = ½ • ¼ = ⅛ 1 10 1− 2 5 = 10 3 5 =

Example 2 Use the properties of radicals to simplify the expression. b.) 5 96 5 3 = 5 • 2 = 10 5 32 ∙ 5 3 5 3 = 2

Example 3 Write the expression in simplest form. a.) 3√104 = 3√8 • 3√13 = 2 3√13

Example 4 Simplify the expression. a.) 7 5√12 – 5√12 = b.) 4( 9 2 3 ) + 8( 9 2 3 ) = 1 6 5√12 12( 9 2 3 )

Warm-Up Use the properties of radicals to simplify the expression. 4 8 ∙ 4 8 3 75 Write the expression in simplest form. 3 104 3 135

Apply Properties of Rational Exponents Section 6-2 Day 2 Apply Properties of Rational Exponents

Example 5 Simplify the expression. a.) 4√625z12 = b.) (32m5n30)1/5 = c.) 3√6x4y9z14 = 5z3 5√32m5n30 = 2mn6 3 √6 • 3√x3 • 3√x • 3√y9 • 3√z12 • 3√z2 = xy3z4 3√6xz2

Example 6 Simplify the expression. a.) 4√12 – 2√75 = b.) 6 3√81 + 7 3√24 = 4•√4 •√3 – 2√25 •√3 4• 2•√3 – 2 • 5 •√3 8√3 – 10√3 = -2√3 6 3√27 • 3√3 + 7 3√8 • 3√3 6 • 3 3√3 + 7 • 2 3√3 18 3√3 + 14 3√3 = 32 3√3

Homework Section 6-2 Pages 424 –425 3, 4, 6, 8, 11, 15, 17, 18, 20, 21, 23, 24, 26 – 28, 33, 35, 36, 40, 43 – 48, 52, 53, 57, 60, 62, 64, 69, 78, 79