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Raising a number to a power is a POWERFUL operation, that's why I for Index comes before Division and Multiplication in the order of operations you know as BIDMAS. This quiz deals with the rules in Math for working with powers.

1.

What is 5^{4} ÷ 5^{2}?

5

25

125

625

2.

What is the value of 2^{4}?

8

16

32

64

2^{4} (two to the power four) = 2 x 2 x 2 x 2

3.

Which of these is not the same as 9^{2} x 81?

9^{4}

3^{8}

8^{9}

6,561

9 x 9 x 9 x 9

4.

What is the value of 2^{-3}?

1/3

1/6

1/8

1/9

A negative power is 1 divided by the positive power

5.

What is one hundred million as a power of 10?

10^{5}

10^{6}

10^{7}

10^{8}

The power of ten is the same as the number of zeroes. 100,000,000 has 8 noughts

6.

What is 4^{3} x 3^{4} as a single power number?

12^{7}

7^{12}

7^{7}

none of these

You can't add the indices to multiply unless both numbers are powers of the same base

7.

What is 3^{2} x 2^{2} as a single power number?

6^{4}

6^{2}

5^{4}

none of these

3 x 3 x 2 x 2 = (3 x 2) x (3 x 2)

8.

What is 16 x 8 as a power of 2?

2^{5}

2^{6}

2^{7}

2^{8}

16 = 2^{4}; 8 = 2^{3}. To multiply powers of the same number you add the indices

9.

Which of these gives the biggest number?

2^{8}

8^{2}

3^{6}

6^{3}

It's not always obvious which power number is the largest. The best way to check is to use a calculator!

10.

What is 8^{3} as a single power of 2?

2^{6}

2^{7}

2^{8}

2^{9}

8^{3} = (2 x 2 x 2)^{3} = (2^{3})^{3}. To raise a power to a power, multiply the indices

^{(4 - 2)}= 5^{2}