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"
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: 24 = 2 × 2 × 2 × 2 =
_________
 103 = 10 × 10 × 10 =
_________
 33 = 3 × ... =
_________
 46 = 4 × ... =
_________
 19 = 1 × ... =
_________
 56 = 5 ×
_________
Q2)
Simplify the following: 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
_________
 12 × 12 × 12 × 12 × 12
_________
 x × x × x × x × x
_________
 m × m × m
_________
 y × y × y × y
_________
 z × z × z × z × z × z
_________
Q3)
Q3) Complete the following (the first one has been done for you): 102
× 103
= (10 × 10)×(10 × 10 × 10) = 105
_________

103 × 104 =
_________
 104 × 102 =
_________
 105 × 103 =
_________
 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):
24 ÷
22 =
(2 × 2 × 2 × 2) / (2 × 2) = 22
_________

25 ÷
22
= (2 × 2 × 2 × 2 × 2) / (2 × 2) =
_________
 45
÷ 43
= (4 × 4 × 4 × 4 × 4) / (... =
_________

85 ÷
82 =
_________

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? 24
× 26
= 210
_________

22
× 23
× 24
= 29
_________

23
× 22
= 26
_________

410
× 44
× 42
= 418
_________

21
× 23
× 24
= 28
_________

104
× 102
= 108
_________

220
÷ 25
= 24
_________

312
÷ 34
= 38
_________

46
÷ 64
= 42
_________

1020
÷ 103
= 1017
_________

46
÷ (42
× 43)
= 43
_________

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

(34
× 32)
÷ (36
× 33)
_________

(410
× 412)
× 43
_________

102
÷ (103
× 1012)
_________

(36)2
_________

42
× 41 ×
46 ×
(42
÷ 43)
_________

(52 ×
53)
÷ (56
÷ 54)
_________