Download 7-3 Study Guide and Intervention Rational Exponents

NAME
DATE
7-3
PERIOD
Study Guide and Intervention
Rational Exponents
Rational Exponents For any real numbers a and b and any positive integer n,
if an = b, then a is an nth root of b. Rational exponents can be used to represent nth
roots.
!
Square Root
𝑏! = 𝑏
Example 1
!
(6𝑥𝑦)! =
!
Cube Root
𝑏! =
nth Root
𝑏! =
!
𝟏
!
𝑏
𝑏
𝟏
Example 2
Write (𝟔𝒙𝒚)𝟐 in radical form.
6𝑥𝑦
!
!
!
625! =
Definition of 𝑏 !
!
Simplify 𝟔𝟐𝟓𝟒 .
!
𝑏! =
625
!
!
𝑏
625 = 5
= 5∙5∙5∙5
=5
4
Simplify.
Exercises
Write each expression in radical form, or write each radical in exponential form.
!
!
!
2. 5𝑥 !
3. 17𝑦 !
!
4. 12!
5. 19𝑎𝑏 !
6. 17
7. 12𝑛
8. 18𝑏
9. 37
Lesson 7-3
!
1. 14!
Simplify.
10.
!
343
11.
!
1024
13.
!
2401
14.
!
64
16.
!
1331
17.
!
Chapter 7
!
12. 512!
!
15. 243!
!
6561
18. 4096!
17
Glencoe Algebra 1
NAME
DATE
7-3
PERIOD
Study Guide and Intervention
(continued)
Rational Exponents
Solve Exponential Equations In an exponential equation, variables occur as
exponents. Use the Power Property of Equality and the other properties of exponents to
solve exponential equations.
Example
Solve 1024x − 1 = 4.
1024x − 1 = 4
(45)x − 1 = 4
45x − 5 = 41
5x − 5 = 1
5x = 6
!
x=
!
Original equation
5
Rewrite 1024 as 4 .
Power of a Power, Distributive Property
Power Property of Equality
Add 5 to each side.
Divide each side by 5.
Exercises
Solve each equation.
1. 2x = 128
2. 33x + 1 = 81
3. 4x – 3 = 32
4. 5x = 15,625
5. 63x + 2 = 216
6. 45x – 3 = 16
7. 8x = 4096
8. 93x + 3 = 6561
9. 11x – 1 = 1331
10. 3x = 6561
11. 25x + 4 = 512
12. 7x – 2 = 343
13. 8x = 262,144
14. 55x = 3125
15. 92x – 6 = 6561
16. 7x = 2401
17. 73x = 117,649
18. 62x – 7 = 7776
19. 9x = 729
20. 83x + 1 = 4096
21. 133x – 8 = 28,561
Chapter 7
18
Glencoe Algebra 1