year 8 maths

50 Chapter 1 Algebraic techniques 2 and indices
Example 20b
Example 19
6 Simplify the following using the index laws.
a (2 3 ) 2 × (2 5 ) 3 b (5 2 ) 6 × (5 3 ) 2 c (7 4 ) 2 × (7 5 ) 3
d (3 3 ) 6 × (3 2 ) 2 e (2 3 ) 2 × (2 4 ) 3 f (11 2 ) 6 × (11 2 ) 3
g
j
(5 3 ) 4
5 2 h
(2 2 ) 10
(2 3 ) 2 k
(11 7 ) 2
i
(11 3 ) 2
3 20
l
(3 3 ) 5
(11 5 ) 3
11 2
(11 2 ) 10
(11 3 ) 6
7 Simplify the following.
a 3 0 b 5 0 c 3 0 + 5 0
d 3 + 5 0 e (3 + 5) 0 f 3 0 × 5 0
g (3 × 5) 0 h 3 × 5 0 i (35 × 53) 0
PROBLEM-SOLVING AND REASONING
8, 12 8–10, 12, 13
9–11, 13–15
8 Find the missing value that would make the following simplifications correct.
a (5 3 ) □ = 5 15 b (2 □ ) 4 = 2 12
c (3 2 ) 3 × 3 □ = 3 11 d (7 4 ) □ × (7 3 ) 2 = 7 14
9 a Use the fact that (5 2 ) 3 = 5 6 to simplify ((5 2 ) 3 ) 4 .
b Simplify ((5 3 ) 4 ) 5 .
c Put the following numbers into ascending order. (You do not need to calculate the actual values.)
2 100 , (2 7 ) 10 , ((2 5 ) 6 ) 7 , ((2 3 ) 4 ) 5
10 a How many zeros does each of the following numbers have?
i 10 2 ii 10 5 iii 10 6
b How many zeros does the number (10 5 × 10 6 × 10 7 ) 3 have?
11 a Simplify x 3 × x 4 .
b Simplify (x 3 ) 4 .
c Find the two values of x that make x 3 × x 4 and (x 3 ) 4 equal.
12 For this question you will be demonstrating why a 0 should equal 1 for any value of a other
than zero.
5
a State the value of
2
5 2.
b Use the index law for division to write 52
as a power of 5 .
2
5
c Use this method to demonstrate that 3 0 should equal 1 .
d Use this method to demonstrate that 100 0 should equal 1 .
e Explain why you cannot use this method to show that 0 0 should equal 1 .
13 Rose is using her calculator and notices that (2 3 ) 4 = (2 6 ) 2 .
a Explain why this is the case.
b Which of the following are also equal to (2 3 ) 4 ?
A (2 4 ) 3 B (2 2 ) 6 C (4 2 ) 3 D (4 3 ) 2 × (6 2 ) 2
c Freddy claims that (2 5 ) 6 can be written in the form (4 □ ) □ . Find one way to fill in the two
missing values.
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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