Page 24 - 新思维数学学生用书8 样章

1.4 Indices

Exercise 1.4

1 Copy and complete this list of powers of 2.

Power 2 0 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10
Number 1 2 8 64 512

2 Copy and complete this list of powers of 3.

Power 3 0 3 1 3 2 3 3 3 4 3 5 3 6 3 7 3 8
Number 3 27 2187

Think like a mathematician

3 Look at this multiplication: 4 × 16 = 64
You can write all the numbers as powers of 2: 2 × 2 = 2 6
2
4
a Write each of these multiplications as powers of 2.
i 8 × 4 = 32 ii 16 × 8 = 128
iii 4 × 32 = 128 iv 2 × 128 = 256

v 16 × 32 = 512
b Can you see a pattern in your answers? Make a
conjecture about multiplying powers of 2. Tip
Test your conjecture on some more multiplications ‘Generalising’
of your own. means using a

c Make a conjecture about multiplying powers of 3. set of results to
Use some examples to test your conjecture. come up with a
d Generalise your results so far. general rule.

4 Write the answers to these calculations as powers of 6.
a 6 × 6 3 b 6 × 6 c 6 × 6 2 d 6 × 6 3
5
4
2
3
5 Write the answers to these calculations in index form.
a 10 × 10 2 b 20 × 20 c 15 × 15 3 d 5 × 5 3
5
3
5
3
6 a 3 = 6561 Use this fact to find 3 and show your method.
8
9
b 5 = 15 625 Use this fact to find 5 and show your method.
6
7
7 Find the missing power.
a 3 × 3 = 3 5 b 9 × 9 = 9 8
3
3
c 12 × 12 = 12 6 d 15 × 15 = 15 10
4
3

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