Page 40 - Start Up Mathematics_8 (Non CCE)

Example 5: Simplify using the laws of exponent and write the result in exponential form:
–3
8
–7
–3
(a) (5) × (5) (b) (4) × (3) –3 (c) (6) ÷ (6) –3
()4 − 6
–5
3 –2
(d) (2 ) (e) (f) (2) ÷ (2) 3
()5 − 6
–3
m
8
n
Solution: (a) (5) × (5) = (5) 8 + (–3) = (5) 8 – 3 = (5) 5 { (x) × (x) = (x) m + n }
–3
n
n
–3
n
–3
(b) (4) × (3) = (4 × 3) = (12) –3 { (x) × (y) = (xy) }
m
(c) (6) ÷ (6) = (6) –7 – (–3) = (6) –7 + 3 = 6 –4 { (x) ÷ (x) = (x) m – n }
–3
n
–7
mn
m n
3 –2
(d) (2 ) = (2) 3 × (–2) = (2) –6 { (x ) = (x) }
n


()4 − 6  4  − 6  ()x n  x  
(e) =     =   
y
()5 − 6  5    ()y n    
n
–5
m
3
(f) (2) ÷ (2) = (2) –5 – 3 = (2) –8 { (x) ÷ (x) = (x) m – n }
Example 6: 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
n
n
–4
n
Solution: (a) (2) × (5) = (2 × 5) = (10) –4 { (x) × (y) = (xy) }
1  1  4
= =  
10
() 4  10 
×−2)
  3 3  −2  3 3 (
− 
− 
mn
m n
(b)     =   { (x ) = x }
  2    2 
 3 −6  2  6  2 6
− 
− 
=   =   =  
 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)
− 
− 
− 
m
n
=   ×   =   { (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 7: Simplify and write in exponential form:
−3
–4
4
(a) (−8 ) ×   −  1  −3 (b) (–2) × (3) × (5) –4
 2 
− 4
–10
(c)  32  5 (d) {(3) ÷ (3) } × (3) –5 (NCERT)
–7


 243 
32