Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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What is the area of a square with sides of length 2.4 cm?
a. | 2.4 cm2 | c. | 9.6 cm2 | b. | 4.8 cm2 | d. | 5.76
cm2 |
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2.
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What is the volume of a cube with edges of length 8 m?
a. | 1536 m3 | c. | 64 m3 | b. | 384 m3 | d. | 512
m3 |
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3.
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What is  ?
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4.
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Calculate  .
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5.
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Express [(–4)6]4 as a power with a single
exponent.
a. | (–4)24 | c. | (–4)2 | b. | (–4)10 | d. | (–24)4 |
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6.
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What is the next number in the sequence 73, 72,
71, 70, …?
a. | –1 | c. |  | b. | 7–2 | d. | 1 |
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7.
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Which expression represents a negative number?
a. | 2–3 | c. | –30 | b. | (–3)2 | d. | (–3)–1 |
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8.
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Evaluate 20 + 2–4.
a. |  | c. | –8 | b. |  | d. | 8 |
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9.
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Which value of x satisfies the equation x–2 =
 ?
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10.
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Which statement is correct about the expression  when it is
evaluated? a. | The sign is positive. | c. | The expression is equal to 0. | b. | The sign is
negative. | d. | The expression is
undefined. |
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11.
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Which power is equivalent to  ?
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12.
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Which power is equivalent to  ?
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13.
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Which expression cannot be evaluated?
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14.
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The root of a number can be represented by
a. | all exponents | c. | a negative exponent | b. | an integral exponent | d. | a rational
exponent |
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15.
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Simplify  .
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16.
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Jean invests $200 in a fund. The investment doubles in value each year. The
formula A = 200(2)n models the total value of the investment, A, in
dollars, after n years. What is the value of her investment after 4 years?
a. | $3200 | c. | $800 | b. | $1600 | d. | $200 |
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17.
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Which expression has the smallest value?
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18.
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Which of the following is equivalent to  ?
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19.
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Write  as a power with a single positive exponent.
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20.
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Express  as an equivalent radical.
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Short Answer
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1.
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State whether each number is a perfect square or a perfect cube. Show your
work.
a) 576
b) 1369
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2.
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Write and evaluate an expression using exponents for the total volume of each
pair of cubes.
a) Cube A has edges 7.7 cm long and cube B has edges 8.4 cm
long.
b) Cube C has edges 3.8 m long and cube D has edges 3.7 m long.
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3.
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Simplify each expression. Write the answer using positive exponents. Do not
evaluate. a)  b)
(3 3)(3 –6)
c) 
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4.
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Simplify, then evaluate. Express the answer to four decimal places, where
necessary. a) 
b) 
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5.
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Express  as a power with a rational exponent. Do not
evaluate.
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Problem
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1.
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Develop three questions that have a solution of p6. For each
question, choose a different exponent law and apply it.
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2.
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What is the area of the rectangle shown, if x = 9? Express the answer as
a mixed radical and then to two decimal places. 
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3.
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The swing of a pendulum is affected by acceleration due to gravity. The
equation T =  represents the relationship between the time it takes a
pendulum that is 1.0 m long to swing back and forth once and gravitational acceleration. In this
formula, T is time, in seconds, and g is the gravitational acceleration, in metres per
second per second, or metres per second squared. a) The gravitational acceleration at
Earth’s surface is about 9.8 m/s 2. How long would it take the pendulum to swing back
and forth once at Earth’s surface? Express the answer to the nearest tenth of a
second. b) The gravitational acceleration on the moon is about  of the gravitational
acceleration at Earth’s surface. Determine how long it would take the pendulum to swing back
and forth if it were on the moon. Express the answer to the nearest tenth of a second.
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4.
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In dice-rolling game, there are 16 contestants. If the number rolled is even,
the contestant must leave the game. The last one remaining wins the prize. How many rolls are
expected before a winner is declared?
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5.
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Amy was asked to simplify an expression involving powers. Her solution is shown.
 a) Identify the error that Amy made. b) Give the correct
solution.
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