Name: 

Evaluate 0.1⁴.

What is the area of a square with sides of length 7.6 cm?

What is the volume of a cube with edges of length 9 m?

Determine the cube root of 512w³.

Which description about the number 225 is correct?

Evaluate 2⁴ + 2^–4.

Which value of x satisfies the equation x^–2 = ?

What is ?

Which power is equivalent to ?

Which power is equivalent to ?

Which expression cannot be evaluated?

Jean invests $800 in a fund. The investment doubles in value each year. The formula A = 800(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?

Initially, 3 people have a bacterial infection. The next day, every infected person infects one more person. If this pattern continues, how many days will it take for 24 people to be infected?

Household smoke detectors contain 200 mg of a radioactive element that has a half-life of 432 years. To the nearest 10 mg, how much of this element will remain in a smoke detector after 20 years?

Express as a power with a rational exponent.

What is as an equivalent radical?

Which of the following is equivalent to ?

Order these irrational numbers from least to greatest: , , , .

Write as a power with a single positive exponent.

Express as an equivalent radical.

State whether each number is a perfect square or a perfect cube. Show your work.
a) 1024
b) 10 648

Determine the area of a square with each side length.
a) 10 km
b) 20 mm

Simplify .

Simplify each expression. Write the answer using positive exponents. Do not evaluate.
a)
b) (3³)(3^–6)
c)

Is the statement always, sometimes, or never true? Explain your reasoning.

Develop three questions that have a solution of p⁶. For each question, choose a different exponent law and apply it.

The first five numbers in a pattern are 1, 2, 9, 64, and 625.
a) Describe the pattern. Show how the first five terms were calculated.
b) Using a calculator, determine the next three terms.
c) Determine the tenth term.
d) Write an expression for the nth term in the pattern.

Matthew’s pay increases by 10% every month. If his first pay is $400, determine the amount of his pay in month 6.

A company manufactures fences for residential use. The production of fencing can be modelled using the equation s = , where s is the number of sections of fencing produced and h is the number of hours of labour.
a) How many sections will be produced if a crew works a total of 120 h in a day?
b) How many more sections will be produced in 240 h per day?
c) How many hours of labour will be needed if the company wants to maintain a production rate of 49 sections per day?

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/s². 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.