*This Math quiz is called 'Numbers - Indices' and it has been written by teachers to help you if you are studying the subject at middle school. Playing educational quizzes is a fabulous way to learn if you are in the 6th, 7th or 8th grade - aged 11 to 14.*

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Cubed and squared are types of indices. In the Powers quiz you saw how, by writing numbers as powers of a common base, multiplication and division can be turned into addition or subtraction of indices making calculations with large or small numbers easier, as long as you follow the Math rules.

1.

What is the result of 2^{4} x 8^{3}?

1,992

8,192

65,536

99,664

2.

John started a savings account with a deposit of £500 at 1.5% compound interest per year. How much (to the nearest 1p) is the account worth after three years?

£168.75

£522.84

£760.44

£1,522.50

After 1 year 500 x 1.015; after 3 years 500 x 1.015^{3}

3.

What is the result of dividing 25 by 625?

5^{1}

5^{-1}

5^{2}

5^{-2}

25 = 5^{2}; 625 = 5^{4}

4.

A pond plant doubles its surface area every four days. If it covered an area of 20 cm^{2} on 17^{th} June, what is its area on 15^{th} July?

2,560 cm^{2}

2.56 m^{2}

0.256 m^{2}

256 cm^{2}

'30 days hath September, April, June and November .......' so the plant has been growing for 28 = 4 x 7 days; 20 x 2^{7}

5.

What is the result of 2^{7} ÷ 2^{8}?

1/2

2

-1/2

-2

2^{(7 - 8)} = 2^{-1} = 1/2 since the negative power is 1 over the positive power

6.

How many liters will fill a cube of side length 25 cm?

1.25

15.625

25.125

61.25

25^{3} ÷ 1,000 = 5^{6} ÷ 10^{3}. Remember 1,000 cm^{3} = 1 liter

7.

What is 0.2^{4} as a power of 5?

5^{-1}

5^{-2}

5^{-4}

5^{-5}

0.2 = 1/5 = 5^{-1}

8.

What is the result of 16 x 64 as a power of 2?

2^{6}

2^{8}

2^{10}

2^{12}

16 = 2^{4}; 64 = 2^{6}; 16 x 64 = 2^{(4 + 6)}

9.

How many days are there in 2^{9} x 3^{3} x 5^{4} seconds?

30

50

100

125

Divide by 60 x 60 = 2^{4} x 3^{2} x 5^{2} to find the hours, then divide by 24 = 2^{3} x 3^{1} to find days

10.

What index number must follow 3 to give 6,561?

7

8

9

10

6,561 = 81 x 81 = 3^{4} x 3^{4}

The next step is:

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^{3}to a power of 2 before adding the indices