Factors, Powers And Standard Form Worksheet Page 15
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21You can use the laws of indices to understand negative powers.
9 3 9 3 9
_________________________
9
3
4 9
7
5
9 3 9 3 9 3 9 3 9 3 9 3 9
1
_____________
5
9 3 9 3 9 3 9
5 1
__
9
4
Using the laws of indices:
1
___
9
3
4 9
7
5 9
3 2 7
5 9
24
This shows that 9
.
4
9
4
You will meet laws of indices again in Section 15.2.
Example 10
C
Simplify
B
a
8
3
b
3
4
c
2
6
5
3 5
2
3 2
3 2
3
4 3
When you multiply powers of the
a 5
8
3 5
3
5 5
8 1 3
same number you add the indices.
5 5
11
b 2
3
3 2
4
3 2 5 2
3 1 4 1 1
Remember that 2 5 2
1
.
5 2
8
When you divide powers of the same
c 3
2
4 3
6
5 3
2 2 6
number you subtract the indices.
5 3
24
1
___
5
3
4
Exercise 10J
C
1
Write each of these expressions as a single power.
a
6
7
3 6
3
b
4
7
3 4
3
c
5 3 5
3
d
9
3
3 9
3
2
Write each of these expressions as a single power.
a
b
c
d
3
7
4 3
3
6
10
4 6
5
4
17
4 4
12
5
3
4 5
3
Write each of these expressions as a single power.
a
8
4
3 8 3 8
6
b
2
2
3 2
7
3 2
4
c
8
3
3 8
5
3 8
d
9 3 9
3
3 9
4
Write down the value of each of these expressions.
a
b
5
8
4 5
5
4
13
4 4
11
Give your answers
as a whole number.
c
2
10
4 2
6
d
7
6
4 7
3
5
Alison writes that 7
10
4 7
2
5 7
5
.
Is Alison correct? Give a reason for your answer.
172
Factors, powers and standard form
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