fractions & indices. rule 1 : multiplication of indices. a n x a m = a n + m rule 3 : for...
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Fractions & Indices.
34
3
)(12
42
d
dd
)()(
)()(43
4325
rr
rr
23 23 )))(27(( w
Rule 1 : Multiplication of Indices.
a n x a m = a n + m
Rule 3 : For negative indices:.
a - mma
1
Rule 2 : Division of Indices.
a n a m = a n - m
Revision.
The next two slides are a revision of the basic rules of Index Numbers. If they are not familiar to you , then you require to go over the “Rules Of Indices” PowerPoint presentation again.
Summary Of The Rules Of Indices.Rule 1 : Multiplication of Indices.
a n x a m = a n + m
Rule 2 : Division of Indices.
a n a m = a n - m
Rule 3 : For negative indices:.
a - m
ma
1
Rule 4 : For Powers Of Index Numbers.
( a m ) n = a m n
Rule 5 : For indices which are fractions.
nn aa 1
(The nth root of “a” )
Rule 6 : For indices which are fractions.
(The nth root of “a” to the power of m)
mnn
m
aa )(
Applying The Rules With Fractions.
We are now going to look at the rules of indices again but use them with fractions that are obtained from the roots of numbers.
MultiplicationExample 1.
Simplify:3 aa
Solution.3 aa •Change the roots to powers.
3
1
2
1
aa • Select the appropriate rule of indices.
Rule 1 : Multiplication of Indices.
a n x a m = a n + m
•Add the fractions.
6
5
6
23
3
1
2
1
6
5
a56 )( a
Example 2.
Simplify:3543 )()( aa
Solution.
•Change the roots to powers.3543 )()( aa
5
3
3
4
aa • Select the appropriate rule of indices.
Rule 1 : Multiplication of Indices.
a n x a m = a n + m
•Add the fractions.
15
29
15
920
5
3
3
4
15
29
a2915 )( a
Division.Example 1.
Simplify:
3 gg Solution.
•Change the roots to powers.3 gg
3
1
2
1
gg • Select the appropriate rule of indices.
Rule 2 : Division of Indices.
a n a m = a n - m
•Subtract the fractions.
6
1
6
23
3
1
2
1
6
1
g6 g
Example 2.
Simplify:2534 )()( dd
Solution.2534 )()( dd •Change the roots to powers.
5
2
4
3
dd • Select the appropriate rule of indices.
Rule 2 : Division of Indices.
a n a m = a n - m
•Subtract the fractions.
20
7
20
815
5
2
4
3
20
7
d720 )( d
Multiplication & DivisionExample 1.
Simplify:
23 )( a
aa
Solution.
23 )( a
aa
•Change the roots to powers.
3
2
2
1
a
aa
• Select the appropriate rule of indices.
Rule 1 : Multiplication of Indices.
a n x a m = a n + m
Rule 2 : Division of Indices.
a n a m = a n - m
•Calculate the fractions.
2
3
2
11
6
5
6
49
3
2
2
3
6
5
a 56 )( a
Example 2.Simplify:
)()(
)()(43
4325
rr
rr
Solution.
)()(
)()(43
4325
rr
rr
•Change the roots to powers.
4
1
2
3
3
4
5
2
rr
rr
• Select the appropriate rule of indices.
Rule 1 : Multiplication of Indices.
a n x a m = a n + m
Rule 2 : Division of Indices.
a n a m = a n - m
•Calculate the fractions.
15
26
15
206
3
4
5
2
4
7
4
1
4
6
4
1
2
3
60
1
60
105104
4
7
15
26
60
1
rRule 3 : For negative indices:.
a - mma
160
60
1
11
rr
Example 3.Simplify:
34
3
)(12
42
d
dd
Solution.
34
3
)(12
42
d
dd
4
3
3
1
2
1
12
42
d
dd
4
3
3
1
2
1
12
8
d
dd
4
3
6
5
12
8
d
d
3
2 4
3
6
5
d
3
2 12
1
d
3
)(2 12 d
Example 4.Simplify:
kk
kk
3)(4
2)(53
334
Solution.
kk
kk
3)(4
2)(53
334
2
1
3
1
34
3
12
10
k
k
6
5
4
15
6
5
k
k
6
5 6
5
4
15
k
6
5 12
1045
k
6
5 12
35
k
6
)(5 3512 k
Power To The Power.Example 1.Simplify:
)4( 3
2
a
Solution.
)4( 3
2
a
•Change the roots to powers.
2
1
3
2
)4( a
• Select the appropriate rule of indices.
Rule 4 : For Powers Of Index Numbers.
( a m ) n = a m n
2
1
3
2
2
1
)()4( a
•Multiply the fractions.
3
1
6
2
23
12
2
1
3
2
3
1
2a32 a
Example 1.Simplify:
23 23 )))(27(( wSolution.
23 23 )))(27(( w
•Change the roots to powers.
3
2
3
2
)27( w
• Select the appropriate rule of indices.
Rule 4 : For Powers Of Index Numbers.
( a m ) n = a m n
)()27( 3
2
3
2
3
2
w
•Multiply the fractions.
9
4
3
2
3
2
9
4
9w49 )(9 w
What Goes In The Box ?Simplify the expressions below :
34 43 aa (1) (2) )(5)(10 33 aa
(3)42
23
62
)(43
aa
aa
712 )(12 a76 )(2 a
12 13
1
a
(4) 33 4 )(27 a
43 a