1. 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

2. 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. 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

4. 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 =
3 𝑥 2
𝑥 ∙ 𝑥 = 𝑥 =𝑥
=𝑥 7 6
= 6 𝑥 7

5. 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 𝑥 6 4
𝑏) 4 𝑥 𝑥 6
= 𝑥 2 𝑥 3 2
= 𝑥 2− 3 2
= 𝑥 4 2 − 3 2
= 𝑥 1 2
= 𝑥

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

7. Example 3: Let’s Try More..B)

8. Example 4…Let’s try more…B) C)

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