Name: 

Evaluate 0.1⁴.

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

Determine the cube root of 512w³.

Calculate .

Express [(–8)⁸]⁵ as a power with a single exponent.

One side of a square is 15g in length. What is the area of the square?

What is the next number in the sequence 3³, 3², 3¹, 3⁰, …?

What is ?

The root of a number can be represented by

Eric deposits $0.01 into a bank account that doubles the amount of money in the account every year. After 1 year the value of the account is $0.02, and after 2 years it is $0.04. What will the value of the account be after 12 years?

For what value of x do 4^x, 2^x, and have the same value?

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 an equivalent mixed radical.

Evaluate .

Which expression has the smallest value?

Which of the following is equivalent to ?

What is as an equivalent radical?

Which of the following is equivalent to ?

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

Express 333 as a sum of powers of 3.

Evaluate using a calculator. Express the answer to four decimal places, where necessary.
a) (6²)(6^2.3)
b)
c)

Express each entire radical as a mixed radical in simplest form.
a)
b)
c)

What is expressed as a radical with positive exponents?

Jason used the number 3 as the base of powers to make the following expression equal to 0.
3³ – (3¹)(3²) = 0
a) Use a combination of four 3s as bases to make an expression equal to 0.
b) Use a combination of five 3s as bases to make an expression equal to 0.
c) Use a combination of six 3s as bases to make an expression equal to 0.

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.

In dice-rolling game, there are 8 contestants. If the number rolled is odd, the contestant must leave the game. The last one remaining wins the prize. How many rolls are expected before a winner is declared?

Hannah is a doctor who needs to determine when she can administer a second dose of a particular drug to her patient. She can model the concentration of the drug in the patient’s bloodstream using the formula C = , where
• C is an estimate of the remaining concentration of the drug in the bloodstream, in milligrams per litre of blood,
• C₀ is the initial concentration of the dose given, and
• h is the time, in hours, since the dose was administered.
How long will it take for a concentration of 100 mg/L to be reduced to 30 mg/L remaining in the bloodstream? Express the answer to the nearest hour.

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.