Page 41 - Start Up Mathematics_8 (Non CCE)


− 
n
n
n
−3
Solution: (a) (−8 ) ×   −  1  −3 = −×8  1  −3 { (x) × (y) = (xy) }


 2    2 
) 1
) 1
 (−8 ) × (−  −3  (−4 ) × (−  −3  4 − 3 − 3
=   =   =   = 4 ()
 2   1   1 
–4
–4
4
n
n
n
4
(b) (–2) × (3) × (5) = (–2) × (3 × 5) –4 { (x) × (y) = (xy) }
4
= (–2) × (15) –4
n


− 
4

= (−2 ) × 1 = (−2 ) 4 =  2  4   ()x n n =  x 


 
15
() 4 () 4  15    ()y  y 
15

− 4 − 4 5 − 4 n

2 

 32  5  () 5 5   2   5  ()x n  x 

(c)   =   =      =   
 243  3 () 5    3     ()y n  y 

4 
2
  5 ×    − 5    2  − 4 m n mn
=   =   { (x ) = (x) }
 3   3 
m
n
–10
–7
–5
(d) {(3) ÷ (3) } × (3) = {(3) –7 – (–10) } × (3) –5 { (x) ÷ (x) = (x) m – n }
= {3 –7 + 10 } × (3) –5
n
m
3
–5
= (3) × (3) = (3) 3 + (–5) { (x) × (x) = (x) m + n }
= (3) –2
Example 8: Simplify: −1
2

2

 2  3  2  − 2    1   − 2 1     −   −2 
1
(a)   ×   ×     × (b)      
 3   3     2    24      6     
 − 3 − 3  − 3
1 

1 

1 

(c)   −    ÷  

5
  4   3   

1 

Solution: (a)  2  3 ×  2  − 2 ×   2  − 2 1 =  2  3 +− ( 2) ×  1  2 ×− ( 2) × 1

 ×
 
 
 
 
 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 32 4 4
2
2
= = = =
324× 324 33× 9
×
  2  −2  −1  2  ( −2) ××− ( 1 )
1
1
mn
m n
(b)      −    =     −   { (x ) = (x) }




     6         6   
  −  1 2  2  −  1 2 × 2
mn
m n

=    =   { (x ) = (x) }
  6    6 
33