Bell Ringer Mrs. Rivas 1. 𝟑 𝟑𝟐 𝒙 𝟒 A. 𝟔 𝒙 𝟐 𝒚 𝟐 𝟑𝒚 2. 𝒙 𝟒 =𝟖𝟏 B.−𝟒 Ida S. Baker H.S. Bell Ringer Match each word in Column A with the matching polynomial of Column B. Column A Column B 1. 𝟑 𝟑𝟐 𝒙 𝟒 2. 𝒙 𝟒 =𝟖𝟏 3. 𝒙 𝟒 =−𝟏𝟐𝟗𝟔 4. 𝟏𝟒 𝒙 𝟕 𝒚 𝟗 𝟕 𝒙 𝟒 𝒚 𝟔 5. 𝒙 𝟑 =−𝟔𝟒 6. 𝟒 𝒙 𝟐 𝒚 𝟑 ∙ 𝟐𝟕 𝒙 𝟐 𝒚 𝟐 A. 𝟔 𝒙 𝟐 𝒚 𝟐 𝟑𝒚 B.−𝟒 C. 𝟐𝒙 𝟑 𝟒𝒙 D. 𝟑 E.𝟐 𝒙 𝟑 𝒚 𝟑 F. 𝑵𝒐 𝒓𝒆𝒂𝒍 𝒓𝒐𝒐𝒕

Rational Exponents Mrs. Rivas Section 6-4 Part I Ida S. Baker H.S. Objective: To use rational exponents. Essential Question: What is a rational exponent? Answer: A rational exponent is an equivalent form of a radical expression.

𝒂 𝒎 𝒏 = 𝒏 𝒂 𝒎 = 𝒏 𝒂 𝒎 Rational Exponents Mrs. Rivas Section 6-4 Part I Ida S. Baker H.S. Objective: To use rational exponents. 𝒂 𝒎 𝒏 = 𝒏 𝒂 𝒎 = 𝒏 𝒂 𝒎

Rational Exponents Mrs. Rivas Example # 1 Section 6-4 Part I Rational Exponents Mrs. Rivas Ida S. Baker H.S. Example # 1 Simplifying Expressions with rational exponents. What is the simplest form of each expression? 𝟐𝟏𝟔 𝟏 𝟑 A B 𝟕 𝟏 𝟐 ∙ 𝟕 𝟏 𝟐 𝟐𝟏𝟔 𝟏 𝟑 = 𝟑 𝟐𝟏𝟔 𝟕 𝟏 𝟐 ∙ 𝟕 𝟏 𝟐 = 𝟕 ∙ 𝟕 = 𝟑 𝟐∙𝟐∙𝟐∙𝟑∙𝟑∙𝟑 = 𝟒𝟗 =𝟔 =𝟕 Note: exponent of 1 2 is the same as Note: exponent of 1 3 is the same as 3

Rational Exponents Mrs. Rivas Example # 1 Section 6-4 Part I Rational Exponents Mrs. Rivas Ida S. Baker H.S. Example # 1 Simplifying Expressions with rational exponents. What is the simplest form of each expression? 𝟓 𝟏 𝟒 ∙ 𝟏𝟐𝟓 𝟏 𝟒 C 𝟓 𝟏 𝟒 ∙ 𝟏𝟐𝟓 𝟏 𝟒 = 𝟒 𝟓 ∙ 𝟒 𝟏𝟐𝟓 = 𝟒 𝟓∙𝟓∙𝟓∙𝟓 =𝟓 Note: exponent of 1 4 is the same as 4

Rational Exponents Mrs. Rivas You Do It Section 6-4 Part I 𝟔𝟒 𝟏 𝟐 A Ida S. Baker H.S. You Do It Simplifying Expressions with rational exponents. What is the simplest form of each expression? 𝟔𝟒 𝟏 𝟐 A 𝟑 𝟏 𝟐 ∙ 𝟏𝟐 𝟏 𝟐 B 𝟏𝟏 𝟏 𝟐 ∙ 𝟏𝟏 𝟏 𝟐 C 𝟖 𝟏𝟏 𝟔

𝒂 𝒎 𝒏 = 𝒏 𝒂 𝒎 Rational Exponents = 𝟏 𝒙 𝟏 𝟑 = 𝟏 𝟑 𝒙 1) 𝒙 𝟐 𝟗 2) 𝒙 −𝟏 𝟑 Section 6-4 Part I Rational Exponents Mrs. Rivas Ida S. Baker H.S. Example # 2 Converting between exponential and radical form. 𝒂 𝒎 𝒏 = 𝒏 𝒂 𝒎 = 𝟏 𝒙 𝟏 𝟑 = 𝟏 𝟑 𝒙 1) 𝒙 𝟐 𝟗 2) 𝒙 −𝟏 𝟑 = 𝟗 𝒙 𝟐 = 𝟏 𝒚 𝟕 𝟐 = 𝟏 𝒚 𝟕 = 𝒚 −𝟕 𝟐 3) 𝒚 −𝟑.𝟓

𝒏 𝒂 𝒎 =𝒂 𝒎 𝒏 Rational Exponents 1) 𝟗 = 𝟗 𝟏 𝟐 2) 𝟑 𝒙 𝟐 = 𝒙 𝟐 𝟑 3) 𝒂 𝟑 Section 6-4 Part I Rational Exponents Mrs. Rivas Ida S. Baker H.S. Example # 3 Converting between exponential and radicals form. =𝒂 𝒎 𝒏 𝒏 𝒂 𝒎 1) 𝟗 = 𝟗 𝟏 𝟐 2) 𝟑 𝒙 𝟐 = 𝒙 𝟐 𝟑 3) 𝒂 𝟑 = 𝒂 𝟑 𝟐 4) 𝟑 𝒂 𝟐 = 𝒂 𝟐 𝟑