Page 23 - 新思维数学学生用书8 样章

1 Integers

1.4 Indices

In this section you will … Key words

• use positive and zero indices to represent numbers and generalise

in multiplication and division. power

In this section you will investigate numbers written as powers.
Look at these powers of 5
n 0 1 2 3 4 5

5 n 25 125 625 3125

So 5 = 5 × 5 × 5 = 125 and 5 = 5 × 5 × 5 × 5 = 625 and so on.
4
3
As you move to the right the numbers in the bottom row multiply by 5.
As you move to the left the numbers in the bottom row divide by 5.
3125 ÷ 5 = 625, 625 ÷ 5 = 125, 125 ÷ 5 = 25

If you continue to divide by 5, 25 ÷ 5 = 5 so 5 = 5
1
There is another number missing in the table. What is 5 ?
0
Divide by 5 again: 5 = 5 ÷ 5 = 5 ÷ 5 = 1
1
0
So 5 = 1
0
If n is any positive integer then n = 1
0
Worked example 1.4

a Show that 7 = 343
3
b Work out

i 7 4
ii 7 0

Answer
×=
a 7 =× 49 7 343
3
777×=
×
4
b i 7 = 7 × = 343 7 = 2401
3
7
ii 7 = 1
0

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