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Cubes and Higher Powers
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Cubes and Higher Powers
Work out each answer carefully. Show your method where asked. Remember that an exponent tells you how many times to use the base as a factor.
Cubes and cube roots
A cube power uses the same number as a factor three times: 4³ = 4 × 4 × 4.
1.Evaluate 4³.
- 12
- 16
- 64
- 81
2.Which multiplication shows 6 cubed?
- 6 × 3
- 6 × 6
- 6 × 6 × 6
- 3 × 3 × 3 × 3 × 3 × 3
3.Calculate 7³. Write the repeated multiplication as well as the answer.
4.Find the cube root of 125. In other words, what number cubed equals 125?
5.Complete the cube-number sequence: 1³ = __, 2³ = __, 3³ = __, 4³ = __, 5³ = __.
6.Match each power with its value.
- 2³
- 3³
- 4³
- 5³
- 6³
- 27
- 64
- 216
- 8
- 125
Higher powers and applications
For example, 2⁴ means 2 × 2 × 2 × 2.
7.Work out 3⁴. Show the repeated multiplication.
8.Calculate 2⁵.
- 10
- 16
- 32
- 64
9.Fill in the missing exponent in each equation: 2^__ = 32; 3^__ = 27; 4^__ = 64; 5^__ = 625.
10.A cube-shaped gift box has edges that are each 8 cm long. Use volume = side length³ to find its volume.
11.Which is greater, 2⁶ or 4³? Calculate both powers to support your answer.
12.A display is built as a cube with 9 small cubes along each edge. How many small cubes make up the whole display?
13.Explain what the exponent means in 7⁴, then write 7⁴ as repeated multiplication.
14.Find the missing base: __³ = 216.
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