year 8 maths

46 Chapter 1 Algebraic techniques 2 and indices
4 a Calculate the value of:
i 2 2 ii 2 3 iii 2 5 iv 2 6
b Is 2 2 × 2 3 equal to 2 5 or 2 6 ?
5 a Calculate the value of:
i 5 6 ii 5 2 iii 5 3 iv 5 4
b Is 5 6 ÷ 5 2 equal to 5 3 or 5 4 ?
6 a Write 8 3 in expanded form.
b Write 8 4 in expanded form.
c Write the result of multiplying 8 3 × 8 4 in expanded form.
d Which of the following is the same as 8 3 × 8 4 ?
A 8 12 B 8 5 C 8 7 D 8 1
Example 17a
Example 17b,c
Example 18
7 Simplify the following, giving your answers in index form.
a 4 3 × 4 5
b 3 10 × 3 2
c 2 10 × 2 5 × 2 3
d 7 2 × 7 × 7 3
8 Simplify the following using the index law for multiplication.
a 2 3 × 2 4 b 5 2 × 5 4
c 7 10 × 7 3 d 3 7 × 3 2
e 3 2 × 3 4 × 3 3 f 7 2 × 7 4 × 7 3
g 2 2 × 2 3 × 2 4 h 2 10 × 2 12 × 2 14
i 10 × 10 3 j 6 2 × 6
k 5 4 × 5 3 × 5 l 2 2 × 2 × 2
9 Simplify the following using the index law for division.
a
e
3 5
3 2 b
7 5
7 3 f
12 10
c
12 4
3 10
g
3 5
5 10
5 3 d
2 3 × 5 10
2 2 × 5 4 h
2 10
2
2 4 × 5 3
2 2
PROBLEM-SOLVING AND REASONING
10–12 10, 12, 13
11–14
10 Tamir enters 2 10000 ÷ 2 9997 into his calculator and gets the error message ‘Number Overflow’
because 2 10000 is too large.
a According to the second index law, what does 2 10000 ÷ 2 9997 equal? Give your final answer as
a number.
b Find the value of (5 2000 × 5 2004 ) ÷ 5 4000 .
c What is the value of 3700 × 3 300
3 1000 ?
11 A student tries to simplify 3 2 × 3 4 and gets the result 9 6 .
a Use a calculator to verify this is incorrect.
b Write out 3 2 × 3 4 in expanded form, and explain why it is not the same as 9 6 .
c Explain the mistake the student has made in attempting to apply the first index law.
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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