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Cubes and Higher Powers

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Cubes and Higher Powers

Use the index to work out how many times the base is multiplied by itself. Show working for calculations and give units where needed.

Understanding Powers and Cubes

A power is a way to show repeated multiplication of the same base. The base is the number being multiplied; the index tells how many factors there are.

1.In 6³, how many times is 6 used as a factor?

2.In 9², identify the base and the index.

3.Write 4³ as a multiplication of equal factors. Do not calculate.

4.Write 5⁴ as a multiplication of equal factors. Do not calculate.

5.Write 8² as a multiplication of equal factors. Do not calculate.

6.Calculate 1³.

7.Calculate 2³.

8.Calculate 3³.

9.Calculate 4³.

10.Calculate 5³.

11.Calculate 2⁴.

12.Calculate 3⁴.

13.Calculate 1⁴.

Working with Higher Powers

14.Which option lists all the expressions with a value of 64?

8²
4³
2⁶
All three expressions

15.Calculate 6².

16.Calculate 7².

17.Calculate 8².

18.Calculate 9².

19.Calculate 10².

20.Work out 2⁵.

21.Work out 3⁵.

22.Work out 10³.

23.Work out 10⁴.

24.Compare 3⁴ and 4³. Which is greater? Include both values to support your answer.

25.Compare 2⁶ and 6². Which is greater? Include both values to support your answer.

Problem Solving with Powers

26.A cube has edges 8 cm long. Find its volume using a power and give your answer in cubic centimetres.

27.Complete the sequence of powers of ten: 10¹ = 10, 10² = 100, 10³ = ____, 10⁴ = ____, 10⁵ = ____. Then describe how the value changes at each step.

28.Find the index n if 2ⁿ = 32.

29.A culture starts with 2 bacteria and doubles once every hour. How many bacteria are there after 4 hours? Write the calculation as a power and give the total.