Www.mathsrevision.com More Rules By the division rule Fractions as Indices S4 Credit.
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www.mathsrevision.com www.mathsrevision.com More Rules 3 5 a a a a a = a a a a a 2 1 = a -n n 1 = a a 3 - 5 = a By the division rule 3 5 a a -2 = a Fractions as Indices S4 Credit
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Transcript of Www.mathsrevision.com More Rules By the division rule Fractions as Indices S4 Credit.
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More Rules3
5
aa
a a a=a a a a a
2
1=a
-nn
1 = a
a3 - 5= a
By the division rule3
5
aa
-2= a
Fractions as IndicesS4 Credit
ww
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More Rules5
5
aa
a a a a a=a a a a a
= 1
0 a =1 5
5
aa
5 - 5= a 0= a
Fractions as IndicesS4 Credit
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What Goes In The Box ?
9a3
S4 Credit
Re-write each with positive indices
-3
9a
-45d
4
5d
-3
74m
37m4
-12h2h
6
-2 -3
ww w
w1
16
3 3
6a2a 3a
1
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More Rules
35a 5 5 5= a a a 5 + 5 + 5 15=a a
m n mn(a ) = a
53a 3 3 3 3 3= a a a a a 3 + 3 + 3 + 3 + 3 15=a a
Fractions as IndicesS4 Credit
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What Goes In The Box ?
(b3)5 =
(y9)-5 =
b15
y-45
S4 Credit
(2m4)2 =
(10s2)3
=
4m8
1000s6
2
-3
14m
6m16
3
4
53x
12
12527x
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1 1 1 1 +
2 2 2 2= a a = a = a
Fractions as Indices
a a = a
12a = a
S4 Credit
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Fractions as Indices
1 1 1 1 1 1+ + 13 3 3 3 3 3a a a = a = a = a
13 3a = a
13 3 3a a a = a = a
S4 Credit
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Fractions as Indices
1nn a = a
In general we have
S4 Credit
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Fractions as Indices
n n m nmm a = a = a
Final Rule
S4 Credit
Examples:
36 1. 361
2 6
643 2. 64
1
3 4
149
1
2
3. 49
1
2
149
83
4.
18
1
3
2
Examples:
17
8
1
3
2. 274
3
Examples:
273 4
1. 363
2
3 4
81
36 3 6 3
216
3. 813
4 814 3 3 3
27
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Fractions as Indices
Examples : Simplify the following
238 3
a
a
34
14
a
2a
23 8
22 = 4
11 3= a ÷ a
1 21 -
3 3= a = a
3 1 -
4 4a2
1 2a
2
S4 Credit
ww
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Fractions as Indices
nn m nm m a = a = a
Examples
834 y
244= y 6= y
34 16 34= 16 3= (2) = 8
S4 Credit
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Fractions as Indices
nn m nm m a = a = a
Examples
53 27
53
1=
27
42 3 2a b 8 12= 16a b
53 27
1=
531
= 2431
=
4 8 12 = 2 a b
S4 Credit
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Fractions as Indices
Example : Change to index form
-3
2
5a
1
-4 3 3m3
3 4
3=
m
1 43 3 = 3 m
12-3
2 =
5a1 32 2
2 =
5 a 1
25
322a
=
Example : Change to radical sign √
34
3=
m
S4 Credit
Examples: Simplify each expression
x1
2
3
4
1
5
x10
20
15
20
4
20 x29
20
x1
2 x3
4 x1
5
x20
20 x9
20 x x920
Remember we add exponents
