25.3 Working with fractional indices
25.3
Working with fractional indices
Why do this?
Objective
Fractional indices are used when you model the
You know the meaning of fractional indices.
rates at which things vibrate, such as your voice box.
Get Ready
Work out
___
__
____
3
3
1.
100
2.
8
3.
√
√
√
27
Key Points
Indices can be fractions. In general,
1
__
__
n
a
a
n
√
In particular, this means that
1
1
__
__
__
__
3
a
a and a
a
2
3
√
√
Example 11
Find the value of the following
1
__
1
__
a
2 5
b
(1000 )
c
16
3
0.25
2
___
__
1
2 5
25
a
√
2
The square root of 25 is 5 because 5 5 25.
5
_______
__
1
The cube root of 1000 is 10 because
3
b
(1000 )
√
1000
3
10 10 10 1000.
10
__
1
__
1
Change the decimal into a fraction 0.25
.
c
16
1 6
0.25
4
4
__
1
a
n
Use the rule
.
1
____
a
n
__
1
1 6
4
1
___
__
1
_____
4
1 6
√
16 2
4
___
4
√
16
because 2
4
16
1
__
2
_
2
_
3
Example 12
Work out the value of
a
8
b
1 6
3
4
__
__
2
1
a
m
n
a
mn
Use the rule (
)
.
a
8
( 8
)
2
3
3
Work out the cube root of 8 fi rst.
2
2
Then square your answer.
4
1
__
3
____
b
1 6
4
__
3
1 6
4
1
Examiner’s Tip
______
__
a
1
n
__
Use
.
1
(1 6
)
3
4
a
n
It is easier to work out the root
1
___
3
2
fi rst as this makes the numbers
1
__
smaller and easier to manage.
8
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