Page 42 - Start Up Mathematics_8 (Non CCE)


−1

 −  1 4 () 4   x  n x () n 
=   =     = 
y
 6  6 () 4     y () n  
1
=
1296

−
   1  − 3  1     − 3    4  3  3     3  x − n y 
3

3

n
5
1


(c)    −    ÷   =    −    ÷      =   
y
x

5
1
   4   3         1   1             
= ()4 { 3 − ()3 } ÷  5  3
3
 
 1 
 1  3
= {64 27− }×  
 5 
x 

1 () 3 37 1×   x n () n 
= 37 × =     = 
5 () 3 125    y () n 
y 
37
=
125
Example 9: Simplify: (NCERT)
25 × ()p − 4 ()3 − 5 × ()10 − 5 × 125
(a) , (p ≠ 0) (b)
5 () − 3 × 10 × ()p − 8 ()5 − 7 × ()6 − 5
25 × ()p − 4 ()5 2 1 () p − 4
Solution: (a) = × ×
5 () − 3 × 10 × ()p − 8 ()5 − 3 10 () p − 8
4
( 3
m
n
= ()5 2 −− ) × 1 × ()p −− ( 8− ) { (x) ÷ (x) = (x) m – n }
10
5
= ()5 2 + 3 × 1 × ()p − 4 + 8 = ()5 × 1 × ()p 4
10 5 × 2
4
= ()5 5 − 1 × 1 × () =p 4 () 5 × ()p 4 = 625 p 4
2 2 2
()3 − 5 × ()10 − 5 × 125 ()3 − 5 × (5 × ) 2 − 5 × ()5 3 ()3 − 5 × ()5 − 5 × ()2 − 5 × ()5 3
(b) = =
()5 − 7 × ()6 − 5 ()5 − 7 × (3 2× ) − 5 () 5 −77 × 3 () − 5 × 2 () − 5
= (3) –5 – (–5) × (5) –5 + 3 – (–7) × (2) –5 – (–5)
n
m
m
n
{ (x) × (x) = (x) m + n and (x) ÷ (x) = (x) m – n }
= (3) –5 + 5 × (5) –2 + 7 × (2) –5 + 5
0
0
5
0
5
= (3) × (5) × (2) = 1 × (5) × 1 { (x) = 1}
5
= (5) = 3,125
–1
–1
Example 10: By what number should (–16) be divided to give the quotient as (–4) ?
Solution: Let the required number be x.
–1
(–16) ÷ x = (–4) –1
1 × 1 = 1
− 16 x − 4
34