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Last Updated August 18, 2021, 1:51 pm
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# Powers and Roots

## Rules for Powers and Indices

The small number floating up high is called the power or index number. Remember the plural of index is indices.
54 = 5 × 5 × 5 × 5 =
We say "five to the power of four"

83 = 8 × 8 × 8 =
we say "eight to the power three" or "eight cubed"

## Q1)

Complete the following:
1. 24 = 2 × 2 × 2 × 2 = _________
2. 103 = 10 × 10 × 10 = _________
3. 33 = 3 × ... = _________
4. 46 = 4 × ... = _________
5. 19 = 1 × ... = _________
6. 56 = 5 × _________

## Q2)

Simplify the following:
1. 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 _________
2. 12 × 12 × 12 × 12 × 12 _________
3. x × x × x × x × x _________
4. m × m × m _________
5. y × y × y × y _________
6. z × z × z × z × z × z _________

## Q3)

Q3) Complete the following (the first one has been done for you):
1. 102 × 103 = (10 × 10)×(10 × 10 × 10) = 105 _________
2. 103 × 104 = _________
3. 104 × 102 = _________
4. 105 × 103 = _________
5. What is the quick method for writing down the final result in b), c) and d)? _________

## Q4)

Complete the following (the first one has been done for you):
1. 24 ÷ 22 = (2 × 2 × 2 × 2) / (2 × 2) = 22 _________
2. 25 ÷ 22 = (2 × 2 × 2 × 2 × 2) / (2 × 2) = _________
3. 45 ÷ 43 = (4 × 4 × 4 × 4 × 4) / (... = _________
4. 85 ÷ 82 = _________
5. What is the quick method for writing down the final result in b), c) and d)? _________

## Q5)

Check each equation. Enter either "true" or "false" or if you prefer, answer as a boolean 1 for true or 0 for false. Which of the following are true?
1. 24 × 26 = 210 _________
2. 22 × 23 × 24 = 29 _________
3. 23 × 22 = 26 _________
4. 410 × 44 × 42 = 418 _________
5. 21 × 23 × 24 = 28 _________
6. 104 × 102 = 108 _________
7. 220 ÷ 25 = 24 _________
8. 312 ÷ 34 = 38 _________
9. 46 ÷ 64 = 42 _________
10. 1020 ÷ 103 = 1017 _________
11. 46 ÷ (42 × 43) = 43 _________
12. 92 × (930 ÷ 925) = 910 _________

## Q6)

Remove the brackets from the following and express as a single power: You can enter the power as a small superscript number using the Maths Pad, or use ^ to mean "to the power of". Eg 2^3 = 2 to the power of 3 = 8
1. (34 × 32) ÷ (36 × 33) _________
2. (410 × 412) × 43 _________
3. 102 ÷ (103 × 1012) _________
4. (36)-2 _________
5. 42 × 4-1 × 46 × (42 ÷ 43) _________
6. (52 × 53) ÷ (56 ÷ 54) _________