1. Section 7.2 Rational Exponents
Integrated Math
Section 7.2
Rational Exponents

2. If a base is raised to a fractional exponent, the denominator is the root of the base, the numerator raises the base to the indicated power.
𝑥 = 𝑥 1 2
3 𝑥 = 𝑥 1 3
5 𝑥 2 = 𝑥 2 5

4. Write in radical form
#1 𝑥 1 3 #2 𝑥𝑦𝑧 2 3 #3 −𝑏 5 4 #4 1 𝑥𝑦 6 5

5. Write in fractional exponent form
#1 𝑤 7 #2 4 (𝑥𝑦) #3 3 (3𝑡) 5

6. Rules for exponents still apply for fractional exponents!!!

7. Multiply “keep the base, add the exponents”
Simplify the exponent if possible.

8. Change radicals to fractional exponents.
Do the indicated operation.
Remember rules for exponents.

9. You need a common denominator to combine these exponents!
Answer is
Answer in radical form is

10. Simplify
#1 𝑥 − 𝑥 −4 3
#2 ( 3 −6 ) 1 2
#3 (4 𝑥 ) −2

11. When simplifying expressions with fractional exponents, take the root of the base first, then raise the result to the power.

12. No calculator simplifying!
# = ? # = ? #3 − = ? #4 81 −1 2 = ? # = ?