Powers – it sounds important, right? Well, they are a big deal in KS3 Maths, especially in algebra. Powers are those small numbers hanging out on the top right of other numbers. Don't let their size fool you – powers pack a punch!

You might hear them called powers, indices, or exponents – but it's all the same cool stuff. Powers are like magic shortcuts, showing a number multiplied by itself. Instead of writing 2 x 2 x 2, we just say 2^{3}. See, powers save time and space!

1.

To what power does 6 need to be raised to give a value of 216?

2.

111 - x^{3} = -105. What is the value of x?

3

6

9

12

3.

If a^{2} = 25, what is the value of a^{4}?

29

50

125

625

a must be 5. a^{4} therefore must be 5 x 5 x 5 x 5

4.

How would you work out the value of 3^{6}?

3 + 6

6 + 3

3 x 6

3 x 3 x 3 x 3 x 3 x 3

Answer is 729

5.

If a = 4 and b = 5, which of these is the largest value?

4a^{2}

3b^{3}

a + a + a + a

b + b + b + b + b + b + b + b + b + b + b + b

3b^{3} = 3 x 125 = 375

6.

If x = 2 and y = 8, what is the answer to 8y / x^{4}?

2

4

8

16

Be careful not to mix up multiplying numbers together (as in 8y) when finding the value of numbers with powers (as in 2^{4})

7.

If a = 3 and b = 10, what is the difference between a^{4} and b^{2}?

17

19

21

23

a^{4} = 3 x 3 x 3 x 3 = 81

8.

1^{9} is 1. What is 9^{1}?

1

9

18

19

9.

In the equation x^{3} + y^{2} - 6 = 51, we are told that the value of x is 2. What is the value of y?

7 or -7

8 or -8

9 or -9

11 or -11

Experiment with different values for y until you find the correct answer

10.

Which of these gives the largest value?

4 + 6

4 x 6

4^{6}

6^{4}

6^{4} = 1,296 whilst 4^{6} = 4,096. We Googled it - did you?

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^{3}= 6 x 6 x 6