Simplifying Expressions with Rational Exponents and Radicals Lesson 3.2 Simplifying Expressions with Rational Exponents and Radicals Please Tear Out Your 3.2 Packet…Pages 107-120

Rational and Irrational Numbers Rational Numbers – Can be written as fractions or ratios. (Ex.: -2, ½, -3/4, 2.5) Irrational Numbers – Cannot be written as fractions. These are decimals that never end as well as non-perfect roots. (Ex.: 𝜋, 5 , 3 12 )

Rules of Exponents Negative Exponent Power of a Quotient Rule Multiplying Same Base Negative Power of a Quotient Dividing Same Base Rational Exponent Rule Power to a Power Rule

Let’s Review… 𝑥 2 3 = 3 𝑥 2 𝑥 1 2 ∙ 𝑥 2 3 = 𝑥 1 2 + 2 3 =𝑥 3 6 + 4 6 Write these in radical form…. 𝑥 2 3 = 3 𝑥 2 𝑥 1 2 ∙ 𝑥 2 3 = 𝑥 1 2 + 2 3   =𝑥 3 6 + 4 6   =𝑥 7 6 = 6 𝑥 7      

Example 1 𝑎) ( 𝑥 2 𝑦) 3 ∙ 4 𝑥 4 = 𝑥 8 ∙𝑦 3 ∙𝑥 4 4 = 𝑥 8 ∙𝑦 3 ∙𝑥 1 Simplify each expression. Assume all variables are positive. 𝑎) ( 𝑥 2 𝑦) 3 ∙ 4 𝑥 4 = 𝑥 8 ∙𝑦 3 ∙𝑥 4 4         = 𝑥 8 ∙𝑦 3 ∙𝑥 1 = 𝑥 9 𝑦 3 = 𝑥 8 4 𝑥 6 4 𝑏) 4 𝑥 8 4 𝑥 6 = 𝑥 2 𝑥 3 2 = 𝑥 2− 3 2 = 𝑥 4 2 − 3 2 = 𝑥 1 2 = 𝑥

Example 2: Simplify each expression. Assume all variables are positive. A) B)

Example 3: Let’s Try More.. B)

Example 4…Let’s try more… B) C)

Assignment #20 Pg. 115 #4-22 even skip #18