1. 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

2. 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.

3. 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

4. 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 is the same as
Note: exponent of is the same as 3

5. 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 is the same as 4

6. 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

7. 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

8. 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