Powers - the word makes you think of something important. And well it should. Powers are a major part of KS3 Maths, especially in the field of algebra. Powers are the small numbers that appear to the upper right of other numbers. Although small they can make a huge difference!

Powers are also known as indices or exponents. Whichever word you use, they all mean the same thing. Powers are an easy way to show that a number has been multiplied by itself. It's easy to write 2 x 2, or even 2 x 2 x 2. But when it comes to longer multiplications powers save both time and space!

How would you write the number 10 billion? Well, 10 billion is 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 10,000,000,000. But, it's much easier and quicker to write 10^{10}. This saves a lot of paper when writing out very large numbers!

Test your powers in this quiz. Take your time and read every question carefully before you submit your answers. Good luck!.

1.

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

17

19

21

23

2.

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

3.

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

4.

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

6^{3} = 6 x 6 x 6

5.

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})

6.

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

7.

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

3

6

9

12

8.

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

9.

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

1

9

18

19

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?

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