From the solution to part (d) above, we can see that (–1) = 1 when n is an even number, and (–1) = –1 when n is an odd number. Can you explain why?
(i) 2 × 3
Solution
6
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For what values of a, is the expression a = a always true for all positive integer n ?
Thinking Time
2
Example
(a) Write each of the following numbers in the form of a .
(i) 125
(ii) 32
(iii) 27
(iv) 10 000
(b) Find the values of the following expressions.
2
(ii) (2 × 3)
2
(iii) –2
4
(iv) (–2)
4
(a) (i) 125 = 5 × 25 = 5 × 5 × 5 = 5
3
(ii) 32 = 2 × 16 = 2 × 2 × 8 = 2 × 2 × 2 × 4 = 2 × 2 × 2 × 2 × 2 = 2
5
(iii) 27 = 3 × 9 = 3 × 3 × 3 = 3
3
(iv) 10000 = 10
4
(b) (i) 2 × 3 = 2 × 3 × 3 = 2 × 9 = 18
2
(ii) (2 × 3) = (6) = 6 × 6 = 36
2
2
(iii) –2 = –(2 ) = –(2 × 2 × 2 × 2) = –16
4
4
(iv) (–2) × (–2) × (–2) × (–2) = 16
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Let’s Try
1. Can you write an expression to represent the multiplication of one thousand of the number 2 together?
2. Write each of the following expressions in the form a . State the base and index of the expression.
(a) (–5) × (–5) × (–5)
(b)
(c) x × x × x × x × x
3. Find the value of the following.
(a) 5
1
(b) 10
(c) l
4
(d) 0
12
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