Page 18 - 新思维数学学生用书9 样章

1.3 Indices

12 Write the answer to each multiplication as a single power.
a 6 × 6 2 b 7 × 7 − 2
−
5
3
c 11 × 11 − 6 d 4 × 4 2
−
−
4
6
13 Find the value of x in each case.
a 2 × 2 = 2 9 b 3 × 3 = 3 4
−
x
x
2
5
c 4 × 4 = 4 − 5 d 12 × 12 = 12 2
−
−
3
x
x
3
Think like a mathematician
14 a Write as a single power:
i 2 ÷ 2 3 ii 4 ÷ 4 2 iii 5 ÷ 5 5 iv 2 ÷ 2 7
10
6
5
5
b The rule for part a is that n ÷ n = n ab when the indices a and b are positive
−
a
b
integers.
Write some examples to show that this rule also works for indices that are
negative integers.
c Give your examples to a partner to check.
15 Write the answer to each division as a single power.
a 6 ÷ 6 5 b 9 ÷ 9 4
2
3
c 15 ÷ 15 6 d 10 ÷ 10 8
2
3
16 Write the answer to each division as a single power.
a 2 ÷ 2 − 3 b 8 ÷ 8 − 2
2
5
c 5 ÷ 5 2 d 12 ÷ 12 − 5
−
−
3
4
17 Write down
a 8 as a power of 2 b 8 as a power of 2
2
−2
c 27 as a power of 3 d 27 as a power of 3
−2
2
e 27 as a power of 9 f 27 as a power of 9.
2
−2
Summary checklist
I can understand positive, negative and zero indices.
I can use the addition rule for indices to multiply powers of the same number.
I can use the subtraction rule for indices to divide powers of the same number.

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