Page 37 - Start Up Mathematics_8 (Non CCE)

1 1 1  n 1 
–4
Solution: (a) (4) = = =   x − = n 
4
4
4 () 4 4 ××× 4 256  x 
n 
 3 −4 1 1   x  n x 

− 
(b)   = =     = 
 5   3 4 (− 3) 4     y 
n
y
− 

  4
 5  5 ()
×××
() 5 4 5555 625
= = =
) ( 3
) ( 3 × −
−
( 3− ) 4 ( 3 × − ) ( 3 × − ) 81
1 1  n 1 
3
(c) = = (2) = 2 × 2 × 2 = 8   x − = n 
2 () − 3 1  x 
2 () 3
n 

x 
(d)  5  − 7 = 1 = 1 = 8 () 7 and  8  − 4 = 1 = 1 = 5 () 4      n = x 


 
 
n
y
 8   5  7 5 () 7 5 () 7  5   8  4 8 () 4 8 () 4     y 

  7   4
 8  8 ()  5  5 ()
8 
5 
−
So,    − 7 ×    − 4 = ()8 7 7 × ()5 4 4 = ) 8 ( 74−   x m = x mn  

74
−
 8   5  ()5 ()8 ()5  x n 
()8 3 8 × 8 × 8 512
= = =
()5 3 5 × 5 × 5 125
Example 2: Write each of the following as a rational number with positive exponent.
−7
−5
–7
–10
(a) {(3) ÷ (3) } × (3) –5 (NCERT) (b)  −  1  ×   −  1 

 5   5 
–10
–7
Solution: (a) {(3) ÷ (3) } × (3) –5

=  1 ÷ 1  × 1  ()x − n = 1 n 


10 
 3 () 7 3 ()  3 () 5  ()x 
10
 1 3 ()  1  3 ()  1
10




=  ×  × =   ×
7
  3 () 7 1  3 () 5   3 ()  3 () 5


2
−
3 ×
= 3 ( 10 7− ) × 1 = () 3 1 = 3 () 3 − 5 = 3 ()   ()x m = ()x m − n 


3 () 5 3 () 5  ()x n 
n

1 1 () 2  1  2  ()x n  x 

= = =     =   
3 () 2 3 () 2  3    ()y n  y 

 −  1 −5  −  1 −7 1 1 1 1
(b)   ×   = × = ×
1
1
 5   5   − 1 5  − 1 7 − () 5 − () 7
    5 7
 5   5  5 () 5 ()
= ()5 5 × ()5 7 = ()5 5 + 7 = ()5 12
−
−
−
−
()1 5 ()1 7 ()1 5 + 7 () 1 12
()5 12
= = () 5 12 { (negative number) even power = positive number}
1
29