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2m+2 * 6m-2 * 102m * 15m-1 * 25m-nSimplify
42m * 32m-3 * 52m -2n+5 * 5-8
=2m+2 * 2m-2 * 3m-2 * 22m * 52m * 3m-1 * 5m-1 * 52m-2n
24m * 32m-3 * 55m -2n+5 * 5-8
=2m+2+m-2 +2m-4m * 3m-2 +m-1-2m+3 * 52m+m-1+2m-2n +8 -5m-+2n
-5
= 20* 30 * 5-1+8 -5 = 52 = 25
Indices & Surds
m+n
am
an
a=*m - na
m
ana=
mn
a
mn
a=}{ a
0=1 provided a0
mn
am
n
aIn general ,n
}{1
a
-na= a = k means a = k
xx
1
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2m+2 * 6m-2 * 102m * 15m-1 * 25m-nSimplify
42m * 32m-3 * 52m -2n+5 * 5-8
=2m+2 * 2m-2 * 3m-2 * 22m * 52m * 3m-1 * 5m-1 * 52m-2n
24m * 32m-3 * 55m -2n+5 * 5-8
=2m+2+m-2 +2m-4m * 3m-2 +m-1-2m+3 * 52m+m-1+2m-2n +8 -5m-+2n
-5
= 20* 30 * 5-1+8 -5 = 52 = 25
Indices & Surds
m+n
am
an
a=*m - na
m
ana=
mn
a
mn
a=}{ a
0=1 provided a0
mn
am
n
aIn general ,n
}{1
a
-na= a = k means a = k
xx
1
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Indices & Surds
Given 3x - 2y = 115
3x-4 +2y-5 = 7, find x & y
satisfying the above
equations
3x-4 + 2y-5 = 7
From this
x- 4 =1
y 5 = 2
x = 5 and y = 7.
Substituting x = 5 and y =7
in the first equation, we
find it is satisfied.
Given 5a + 2b+1 = 189
5a+1 +2b-2 = 633, find x & y
satisfying the above
equations
5a+1 + 2b-2 = 633
From this
b -2 = 3
a+1 = 4
a = 3 and b = 5.
Substituting a = 3 and b =5
in the first equation, we
find it is satisfied.
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Indices & Surds Comparison of Numbers
Which is Greater
2150 3100
(23)50 (32)50(8)50 < (9)50
2150 < 3100
M e t h o d 1
M a k e p ow e r s s a m e
b y c o n s i d e r i n g HCF
Which is Greater
575 650
(53)25 (62)25
(125)25 > (36)25
575 > 650
Which is Greater
264 313 *414
264
= 432
313 < 413
313*414 < 427
264 > 313 *414
Which is Greater
3224 5920
2120 5920
6420 5920
3224 > 5920
Which is Greater
763 1840
(73)21 (182)20
(343)21 > (324)20
Which is Greater
3200 24240
(35)40 (242)20
(243)20 > (242)20
Which is greater
3111 1714
3111 < (25)11 (24)14 > 256
3111 < 1714
M e t h o d 2 . M a n i p u l a t e Po w e r s a n d
B a s e s . c o m p a r e t h e n u m b e r s
>
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Indices & Surds Comparison of Numbers
Which is Greater (1) 89 98 (2) 76 67
Whi le Com par ing Num bers use t he resu l t2 [1+1/n]n 530
3031>3130
15031>15530
10026=426*2526
10425=425*2625
426>425
2526>2625
10026>10425
8117=(89)13
9104= (98)13
89>98
8117>9104
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Indices & Surds Comparison of Numbers
Which is Greater (1) 89 98 (2) 76 67
Whi le Com par ing Num bers use t he resu l t2 [1+1/n]n 530
3031>3130
15031>15530
10026=426*2526
10425=425*2625
426>425
2526>2625
10026>10425
8117=(89)13
9104= (98)13
89>98
8117>9104
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If A = (105)19, B = (100)20, C = (110)18, then which of the
following is true?
(a)B>C>A (b)B>A>C (c)C>B>A (d)A>B>C
(e)C>A>B
Indices & surds
A = 519 *2119 B = 520 * 2020 C = 518 * 2218
2O2O > 2119 > 2218 52O > 519 > 518 B > A >
C
2119
2020< 1 2119 2020
