WJEC MATHEMATICS
INTERMEDIATE
NUMBER
POWERS AND ROOTS
1
Contents
Powers
Power of zero
Fractional Indices
Negative Indices
Reciprocals
Powers of Fractions
Credits
WJEC Question bank
http://www.wjec.co.uk/question-bank/question-search.html
2
Powers
A power (represented by a small superscript numbers) tells you how
many times a number is multiplied by itself.
Examples
21 = 2
22 = 2×2 = 4
23 = 2×2×2 = 8
24 = 2×2×2×2 = 16
25 = 2×2×2×2×2 = 32
Power of 2 is called
'squared'
Power of 3 is called
'cubed'
These are discussed
in the booklet
'Number Properties'
Common exam question
Calculate:
23 ×52
23 = 2×2×2 = 8
52 = 5×5 = 25
8×25 = 200
Exercise N16
Calculate the following
1. 33 ×24
2. 43 ×22
3. 62 ×23
4. 53 ×22
5. 33 ×22
3
Exam Questions N10
1.
2.
3.
4.
5.
4
Power of Zero
ANYTHING TO THE POWER OF ZERO IS
1
Example
360 = 1
Fractional Indices
Some common fractional indices:
• Power of
1
2
means square root
1
492
• Power of
1
3
=7
means cube root
1
643
=4
Exercise N17
Simplify:
1
2
a. 400
1
2
f. 225
1
2
c. 196
d. 36
e. 1
1
3
b. 81
1
2
1
3
1
3
g. 64
i. 360
j. 1440
k. 810
l. 2560
1
3
h. 343
5
Negative powers
If the power is negative, ignore it to answer the question, then flip
your final answer.
If your answer is an integer, when you flip
it, it becomes 'one over' that integer
Example 1
4−2
If we were to ignore the negative sign, we would have 42 = 16.
However, the negative sign means we need to flip our answer.
1
=
16
Example 2
81
−
1
2
1
2
If we were to ignore the negative sign, we would have 81 = 9
However, the negative sign means we need to flip our answer.
1
=
9
The mathematical language for 'flip' is the
RECIPROCAL
Example: The reciprocal of 5 is
Example 2: The reciprocal of
3
4
1
5
4
is
3
Exercise N18
Simplify
1. 3
−3
2. 13
−2
3. 121
−
1
2
4. 27
−
1
3
6
Powers of Fractions
If a power has been raised to a power, that power affects the
numerator and the denominator.
Example 1
23
2 3
8
(3) = 27
33
Example 2
49
1
2
1
492
7
(64) = 8
1
642
Example 3 (If the power is negative)
1
642
1
49 −2
(64)
8
=7
1
492
Exercise N19
2 2
a. (3)
4 3
c. (5)
4
1
2
d. (81)
7 2
b. (9)
16
1
2
e. (36)
1
f.
49 −2
(121)
7
Exam Questions N11
1.
2.
3.
4.
5.
8