year 8 maths

1J
Index laws for multiplication and division
45
Example 17
Using the index law for multiplication
Simplify the following using the index law for multiplication.
a 5 3 × 5 7 × 5 2 b 5 3 × 5 4 c 6 5 × 6 × 6 3
SOLUTION
EXPLANATION
a 5 3 × 5 7 × 5 2 = 5 12 3 + 7 + 2 = 12, so the base 5 appears 12 times,
giving 5 12 .
b 5 3 × 5 4 = 5 7 3 + 4 = 7 , so 5 3 × 5 4 = 5 7 .
c 6 5 × 6 × 6 3 = 6 5 × 6 1 × 6 3 = 6 9 Write 6 as 6 1 , then add the powers.
5 + 1 + 3 = 9, so the final result is 6 9 .
Example 18
Using the index law for division
Simplify the following using the index law for division.
a
5 7
5 3 b
6 20
6 5 c
10 × 5 6
4 × 5 2
SOLUTION
EXPLANATION
5
a
7
5 = 5 3 54 Considering
7
5 = 5 × 5 × 5 × 5 × 5 × 5 × 5
3 5 × 5 × 5
= 5 4
or just 7 − 3 = 4 .
b
c
6 20
6 = 5 615 Use the second index law, so 20 − 5 = 15 .
10 × 5 6
4 × 5 = 10 2 4 × 56
5 2
First separate the numbers into a separate fraction.
= 5 2 × 54
1
= 55
2
Cancel the common factor of 2 and use the second
index law.
Combine the result as a single fraction.
Exercise 1J
UNDERSTANDING AND FLUENCY
1–6, 7–8(½) 4–7, 8–9(½)
7, 8–9(½)
1 Fill in the gaps: In the expression 5 7 the base is ____ and the exponent is ____.
2 Which of the following expressions is the same as 3 5 ?
A 3 × 5 B 3 × 3 × 3 × 3 × 3
C 5 × 5 × 5 D 5 × 5 × 5 × 5 × 5
3 Which of the following is the same as 4 × 4 × 4 ?
A 4 4 B 4 3 C 3 4 D 4 × 3
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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