i.e.nth power of an

1

a a

n

n

̧

̧

¹

·

̈

̈

©

§

1

and nth root of a=an an

1 1

() =na.nth root of

ais written as na.
Example 4. Simplify : (a)^2

1

4

3

7 ˜ 7 (b)^2

1

4

3

( 16 ) y( 16 ) (c)

4

3

3

2

(^10) ̧ ̧
¹
·
̈ ̈
©
§
Solution : (a)^4
5
2
1
4
3
2
1
4
3
7 ˜ 7 7 7

(b) ( 16 ) ( 16 ) ( 2 ) ( 2 ) 2.
( 16 )
( 16 )^4
41
4
1
4 4
1
2
1
4
3
2
1
4
3
2
1
4
(^3) ( 16 )
( 16 ) y
 u
(c) 10 102 10.
1
4
3
3
4 2
3
3
2
(^10) ̧ ̧
¹
·
̈ ̈
©
§ u
Example 5. Simplify : (a)^23
1
( 12 ) u 54 (b)
2
3
2
1
( 3 ) ̧
¹
·
̈
©
§
 u 
Solution : (a)^3
1
2
1
2 3
1
( 54 )
( 12 )
1
( 12 ) u 54 u

.
4
3
4
3
2
3
2
3
3
3
2
2
( 32 )
( 23 )
1
( 3 ) 2
( 2 ) 3
1
( 3 2 )
( 2 3 )
1
3
3
1
2
1
3
2
2
1
3
11
2
11
2
1
1
1
3
1
3
1
2
1
3
1
3
1
3
2
1
2
1
2
3
1
3
2
1
2
u ˜ u
˜
u ˜
˜u
u u
u


(b)
2
3
2
1
( 3 ) ̧
¹
·
̈
©
§
 u  = ̧
¹
·
̈
©
§
̧
¹
·
̈
©
§
   u 
2
1
2
1
( 3 )( 3 )( 3 )

4
27
4
1
 27 u 
Activity : Simplify : (i)
32
24 ˜ 22
(ii)
2
5
2
5
3
2
3
2

̧
¹
·
̈
©
§
̧ u
¹
·
̈
©
§
(iii)^2
1
4
3
8 y 8
To be noticed :

1. Under the condition a! 0 ,az 1 , if ax ay,x y


2. Under the condition a! 0 ,b! 0 ,xz 0 , if ax bx,a b
   Example 6. Solve : 4 x^1 32.