Name: ________________________ Class: ___________________ Date: __________
ID: A
Exponents Test Chapter 4
Multiple Choice
Identify the choice that best completes the statement or answers the question.
7. What is the next number in the sequence 33, 32, 31,
30, …?
a. –1
b. 3–2
1
c.
3
d. 1
1. Evaluate 0.14.
a. 0.4
b. 0.01
c. 0.001
d. 0.0001
2. Which description about the number 225 is
correct?
a. perfect cube
b. perfect square
c. both a perfect cube and a perfect square
d. neither a perfect cube nor a perfect square
8. Which expression is not equal to 4?
27
a.
25
b. (21)(21)
c. (2 + 2)0
3. Which description about the number 3375 is
correct?
a. a perfect cube
b. a perfect square
c. both a perfect cube and a perfect square
d. neither a perfect cube nor a perfect square
4. Calculate (8 + 8) 4 −
a.
b.
c.
d.
b.
c.
d.
−1
1
4
1
9. Which value of x satisfies the equation x–2 = ?
9
a. 18
b. 9
c. 4.5
d. 3
42 − 44
.
2
−120
32888
65656
32632
5. Simplify
a.
d.
1
2
2
9
10. Evaluate 196 .
a. 98
b. 15
c. 13
d. 14
4
(9).
16
729
16
6561
16
144
11. What is
a. 50
b. 11
c. 10
d. 9
6. Which expression represents the volume of a cube
of edge length 5x?
a. (5x)(5x)(5x)
b. 5x + 5x + 5x
c. 6(5x)2
d. 125x2
1
2
100 ?
Name: ________________________
1
3
3
2
ID: A
4
3
12. Simplify [(5 ) ] .
a. 25
a.
b.
3
2
c.
b.
c.
5
3
25
d.
12
5 18
d.
a.
x
−
b.
c.
d.
x
x
x
4
2
24
34
48 to an equivalent mixed radical.
12
12
3
2
1
2
13. Which of the following is equivalent to
−
4
14. Convert
15. What is (3x) as an equivalent radical?
1
?
4
( x )3
a.
b.
4
3
3
4
3
4
3x
3 x
c.
3
2x
d.
3 x
2
4
3
Matching
Match the correct term to each of the following descriptions. A term may be used more than once or not at all.
a. base
e. perfect cube
b. cube root
f. perfect square
c. exponent
g. prime factorization
d. irrational number
h. square root
1. a number that can be expressed as the product of
three equal factors
3. the process of writing a number as a product of its
prime factors
2. one of two equal factors of a number
Match the correct term to each of the following descriptions. A term may be used more than once or not at all.
a. radicand
d. irrational number
b. radical
e. index
c. mixed radical
f. entire radical
7. the product of 1 and a radical
4. a number that cannot be expressed as a terminating
or repeating decimal
5. the number 3 in the expression
3
6. the number 25 in the expression
8. the product of a rational number and a radical
81
3
9. the number 2.236… is an example
25
10. consists of a root symbol, an index, and a radicand
2
Name: ________________________
ID: A
Completion
Complete each statement.
1. When multiplying powers that have the same base,
_________________________ the exponents.
6. 1024 as a power of 4 is
_________________________ .
2. To simplify a power of a power,
_________________________ the exponents.
7. The edge length of a cube with a volume of 343
cm3 is _________________________ .
3. Any non-zero base raised to the exponent of
_________________________ is equal to 1.
8. The value of x that makes
4
3
x
=
27
true is
64
_________________________ .
4. The result of raising a fraction to a negative
exponent is the same as the result of raising the
_________________________ of the fraction to
the corresponding positive exponent.
9. The mixed radical 3 4 5 , when written as an entire
radical, is equal to _________________________ .
1
2
m2
, when expressed as a power, is
n3
_________________________ .
10. The radical
5. The expression 15 is equivalent to the expression
_________________________ .
3
Short Answer
5. Express 333 as a sum of powers of 3.
1. State whether each number is a perfect square or a
perfect cube. Show your work.
a) 1024
b) 10 648
6. Simplify each expression. Write the answer using
positive exponents. Do not evaluate.
(−2.5) 3
a)
(−2.5) −2
b) (33)(3–6)
s 2 t −1
c)
1
2. Determine the area of a square with each side
length.
a) 10 km
b) 20 mm
(s 4 t 4 )
3. Determine the volume of a cube with each edge
length.
a) 17 yd
b) 11 ft
2
7. Express each entire radical as a mixed radical in
simplest form.
a) 45
4. Write and evaluate an expression using exponents
for the total area of each pair of squares.
a) Square A has side lengths of 5.1 m and square B
has side lengths of 3.5 m.
b) Square C has side lengths of 4.3 yd and square
D has side lengths of 9.3 yd.
b)
c)
3
3
40
243
Name: ________________________
ID: A
8. Express each radical as a power.
a)
4
x4
y3
b)
c)
3
9. Is the statement 5 (−x) 5 = x always, sometimes, or
never true? Explain your reasoning.
5
3
7
351
as a power with a rational
10. Express
exponent. Do not evaluate.
64n 4
Problem
1. An open-topped cubical box has a volume of 216
cm3. Determine the total surface area of the five
faces of the box.
2. There are 6 bacteria in a dish at the beginning of an
experiment. The number of bacteria doubles every
2 h. How many bacteria are there after 9 days?
Express your answer in both exponential and
simplified form.
3. Amy was asked to simplify an expression involving
powers. Her solution is shown.
−
1
4
3
3 −0.25
=
3 −0.75 3 −0.75
=3
10
3
−0.25 + (−0.75)
= 3 −1
1
3
a) Identify the error that Amy made.
b) Give the correct solution.
=
4