Download 5.1 Practice B

Name_________________________________________________________
5.1
Date __________
Practice B
In Exercises 1–3, find the indicated real nth root(s) of a.
1. n = 3, a = 343
2. n = 6, a = − 64
3. n = 5, a = − 243
In Exercises 4–9, evaluate the expression without using a calculator.
4. 363 2
7.
5. 163 4
(−125)5 3
8. 256− 5
6.
4
(− 32)2 5
9. 27
−4 3
In Exercises 10–15, evaluate the expression using a calculator. Round your
answer to two decimal places when appropriate.
10. 28−1 5
13. 750− 2
12. 40,3516 7
11. 150 2 5
5
14.
(
5
223
)
3
15.
(
7
− 34
)
5
In Exercises 16 and 17, find the radius of the figure with the given volume.
16. V = 425 in.3
17. V = 1458 m 3
h = 7 in.
r
r
In Exercises 18–23, find the real solution(s) of the equation. Round your answer
to two decimal places when appropriate.
18. 6 x 4 = 60
19. x 5 = − 233
20. x 4 + 19 = 100
21. x 3 + 17 = 57
22. 1 x 4 = 125
5
23. 1 x3 = − 49
7
24. Kepler’s third law states that the relationship between the mean distance d
(in astronomical units) of a planet from the Sun and the time t (in years) it
takes the planet to orbit the Sun can be given by d 3 = t 2 .
a. It takes Venus 0.616 year to orbit the Sun. Find the mean distance of
Venus from the Sun (in astronomical units).
b. The mean distance of Jupiter from the Sun is 5.24 astronomical units.
How many years does it take Jupiter to orbit the Sun?
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Algebra 2
Resources by Chapter
149
Name_________________________________________________________
5.2
Date __________
Practice A
In Exercises 1–6, use the properties of rational exponents to simplify the
expression.
1.
4.
(7 )
2 14
10
14
10
2.
(14 )
5.
65
95
3
15
12
3.
−1 5
6.
5
5
(
7
−3 4
• 71 4
)
−1
In Exercises 7–12, use the properties of radicals to simplify the expression.
3•
7.
10.
4
9 •
4
75
8.
9
11.
3
5
81 •
3
9
128
5
4
9.
4
12 •
4
8
5
12.
80
In Exercises 13–18, write the expression in simplest form.
3
13.
4
208
14.
16.
1
2+ 3
17.
3
9
4
6
4− 5
15.
5
27
18.
8
2 +
5
In Exercises 19–24, simplify the expression.
19. 8 4 2 + 5 4 2
22. 4
18 − 15 2
20. 7 5 13 − 17 5 13
23. 8
7 + 12 63
( ) + 7 (9 )
21. 4 9
24.
4
14
14
405 + 2 4 5
25. The volume of a cube is 80 cubic centimeters.
a. Use exponents to solve the formula for the volume V of a cube with side
length s, V = s 3 , for s.
b. Substitute the expression for s from part (a) into the formula for the surface
area of a cube, S = 6 s 2 .
c. Substitute the volume of the given cube into the formula found in part (b)
to find the surface area, S. Simplify, if possible.
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All rights reserved.
Algebra 2
Resources by Chapter
153
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