Page 36 - ICSE Math 8

n


()4 − 6   −6  ()x n  x  
4
(e) =     =   
5
y
()5 − 6     ()y n    
–5
n
m
3
(f) (2) ÷ (2) = (2) –5 – 3 = (2) –8 { (x) ÷ (x) = (x) m – n }
Example 5: Simplify and write in the exponential form with positive exponent.

   −   −2  5 7  −5
3
3
− 
− 
− 
–4
(a) (2) × (5) –4 (b)     (c)   2  2 ×   2
   2      ÷    
   3
  3
 3

4
–4
–4
–4
n
n
–4
n
Solution: (a) (2) × (5) = (2 × 5) = (10) = 1 =  1  { (x) × (y) = (xy) }


10
() 4  10 
×−2)
  3 3  −2  3 3 (  3 −6  2  6  2 6
− 
− 
− 
− 
m n
mn
(b)     =   =   =   =   { (x ) = x }
  2    2   2   3  3 
− 
  2 5  2 7   2 −5   2 5 − 7   2 −5
− 
− 
m
n
(c)   −  −  ×  −   =    ×   { (x) ÷ (x) = (x) m – n }

 ÷ 
  3   3    3    3    3 
 2 −2  2 −5  2 −+ −2 ( 5)
− 
− 
− 
n
m
=   ×   =   { (x) × (x) = (x) m + n }
 3   3   3 
 2 −−2 5  2 −7
− 
− 
=   =  
 3   3 
n


− 
 3  7  3 7   x  − n  y  
=   =       =   
y
 − 2   2       x  

Example 6: Simplify.
2

 2  3  2  − 2    1   − 2 1   1  − 3  1  − 3   1  − 3
(a)   ×   ×     × (b)    −    ÷  
 3   3     2    24   4   3   
5
 2  3  2  − 2   1  2  − 2 1  2  3 +− ( 2)  1  2 ×− ( 2) 1

Solution: (a)   ×   ×    × =   ×   ×
 3   3    2   24  3   2  24
m
n
m n
mn
{ (x) × (x) = (x) m + n ; (x ) = (x) }
2
1 
=  2  1 ×    − 4 × 1 = 2 × 2 () 4 × 1 = 2 × () 4 × 1 = 2 () 5 × 1
 
 3   2  24 3 24 324× 324×
2
2
2
2 ×××× 2 32 4 4
= = = =
×
324× 324 33× 9

   1  − 3  1     − 3    4  3  3     3   x − n  y 
3


n
−
3
5

1
(b)    −    ÷   =    −    ÷       =   
x
   4   3         1   1         y    
5
1
3
1 
= ()4 { 3 − ()3 } ÷  5  = {64 27− }×    3
3
 
 1   5 
1 () 3 37 1× 37   x n () n 

x 
= 37 × = =     = 
5 () 3 125 125    y () n 
y 
Example 7: Simplify.
25 × ()p − 4 ()3 − 5 × ()10 − 5 × 125
(a) , (p ≠ 0) (b)
5 () − 3 × 10 × ()p − 8 ()5 − 7 × ()6 − 5
24