1. Warm-ups: Simplify the following−
2𝑎 𝑏 2 ∙ 6 𝑎 3 𝑏 2 3− 4−

2. Section 7.6 Rational Exponents
Class notes from ___________
By the end of this section, you will be able to:
Write expression with rational exponents in radical form and vice versa;
Simplify expressions in exponential or radical form.
Assignment Due ___________:
A# 7.6: Page 420 #18-50 even
MUST SHOW WORK TO RECEIVE CREDIT

3. Example #1: Radical and Exponential Forms
Write the following in radical form:
Write the following in exponential form:
a. 𝑥 1 5
d. 8 𝑐 b e
c. 𝑚 2 3
f 𝑥 5 𝑦 7

4. Example #2: Evaluate Expressions with Rational Exponents
Evaluate each expression.
a. 27 − 1 3
d. 81 − 1 4 b e c f

5. Example #3: Real World Example
The radius r of a sphere with volume V is given by 𝑟= 3𝑉 4𝜋
A. Find the radius of a ball whose volume is 77 𝑐𝑚 3
B. Find the radius of a ball whose volume is 52 𝑐𝑚 3

6. Example #4: Simplify Expressions with Rational Exponents
Simplify each expression.
a. 𝑎 ∙ 𝑎 9 4
b. 𝑟 − 4 5
c. 𝑎 ∙ 𝑎 1 4

7. Example #5: Simplify Radical Expressions
Simplify each expression.
c. 𝑦 𝑦 −2 a
b 𝑥 4

8. PRACTICE #5: Simplify Radical Expressions
Simplify each expression.
f. 𝑎 𝑎 −1 d
e 𝑥 3