Name__________________________________
Period________________
Rational Exponents
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Write rational exponents in radical notation and radicals in rational exponential notation.
1) 125 4/3
4
A) 125 3
2)
10
1)
125 4
B)
C)
125 3
D)
3
125 4
x15
A) x3/2
2)
B) x5
C) x2/3
D) x5/2
Perform the indicated operations. Write answers using only positive exponents. Assume variables represent positive real
numbers.
3) 7a4/3 · 7a -13/3
A)
4)
B)
7
a4
C)
a3
49
D) 7a -9
2x1/7
6x1/4
A)
5)
49
a3
3)
4)
1
3x3/28
B)
x3/28
3
C)
1
3x1/28
D)
x1/3
3
x1/2 y3 3
y3/2
A)
x3/2
y9/2
5)
B) x3/2
C) x3/2 y9/2
D) x1/2 y9/2
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Simplify the expression. Assume all variables represent positive real numbers.
6)
3
64k15
6)
-24y5
7)
8)
3 256x4
4x
8)
9)
18x2 y
25
9)
7)
3
1
Simplify the expression involving rational exponents.
8 -2/3
10) 125
10)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Write with radicals. Assume that all variables represent positive real numbers.
11) (7m + n) 8/9
9
A) 7m + n8
11)
B)
8
7m + n9
C)
9
(7m + n)8
D)
8
(7m + n)9
Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all
variables represent positive real numbers.
x1/2 · x3/10 · x2/5
12)
12)
(x2)-1/2
A)
1
x22/7
B)
1
x11/5
C) x22/7
D) x11/5
13) 2k1/8(-8k3/8 - 7k3/4)
13)
A) -16k1/2 + 14k7/8
B) -16k-1/4 + 14k-5/8
C) -16k1/2 - 14k7/8
D) -16k3/64 - 14k3/32
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Write with rational exponents and then apply the properties of exponents. Assume that all radicands represent positive
real numbers. Give answers in exponential form.
4
3
14) x7 · x4
14)
x5
x10
15)
16)
5 4
15)
w
16)
Provide an appropriate response.
17) How many real square roots does any positive number have?
Simplify the radical. Assume that all variables represent positive real numbers.
4
18) 482
19)
8
x20
17)
18)
19)
Simplify the expression involving rational exponents.
20) (-64)1/2
20)
2
Answer Key
Testname: RATIONALEXPONENTSPREAP
1)
2)
3)
4)
5)
D
A
A
A
C
6) 4k5
3
7) -2y 3y2
8) 4x
3x 2y
9)
5
10)
25
4
11) C
12) D
13) C
14) x37/12
15)
1
x5/2
16) w1/20
17) Two
18) 4 3
19) x2 x
20) Not a real number
3