Page 44 - Start Up Mathematics_8 (Non CCE)

m
5
–3
Example 14: Find the value of m for which (5) ÷ (5) = (5) . (NCERT)
–3
m
Solution: (5) ÷ (5) = (5) 5
n
m
⇒ (5) m – (–3) = (5) 5 { (x) ÷ (x) = (x) m – n }
⇒ (5) m + 3 = (5) 5
n
m
⇒ m + 3 = 5 { If (x) = (x) ⇒ m = n}
⇒ m = 5 – 3 = 2
So, m = 2
EXERCISE 2.2

1. Evaluate:

–2
(a) (3) (b) (–5) –4 (c)  −  1  −2 (d)  2  − 3

 
p  4   5 
2. Write the following in the form q :
2
5 
(a)  3  − 1 (b) − ( ) ×6 −1   −1 (c)  3  − 1 ×    − 1
 
 
 
3
 5     5   2 
3. Simplify:
–1 2
–1 –1
–1
–1
–1
–1
–1
–1 –1
–1
(a) {(5) × (4) } (b) {(5) ÷ (6) } (c) {(2) × (3) } × (4) (d) {(4) – (5) } ÷ (3) –1
4. Find the reciprocal of the following:
   1   3  2  − 2  3  − 4  4 −2  4 −3  4 5

−
1
− 
− 
− 
(a)     (b)   ÷   (c)   ×   ÷  

   4    3   2   7   7   7 
5. Write each of the following as a rational number with negative exponent:


3
2
 4  6    2   − 2     3   − 1  3
(a) (7) 4 (b)   (c)     (d)      
 9     3       4   


6. Write each of the following as rational number with positive exponent:  
–5
3
(a)  4  − 3 (b)    1  − 2  3 (c)    3  − 3  − 4 (d) (8) × (8) × (8) –4
  
  
 
 3     5       7  

7. Simplify: −1
2

1
 3  2 1 − 4  7  − 1  3  − 2  2  − 2  1  − 2     −   −2 
(a)   × × 3 () ×   (b)   +   +   (c)      
 2  4 − 4  3   4   3   2     3   
   

1


−
3

3
4 
2  
(
1    
1
−
2
2
3
(d) 5 − ) ×    − 3 (e)    1  − 1 ×− ( 25)  − 1 (f)       ×   2 ÷       3

 
 3     5       3        3  
2


–1
–1
8. By what number should (3) be multiplied to get the product as (–6) ?
 2  − 2  9 −1
− 
9. By what number should   be multiplied to get the product as   ?
 3   4 
 3 −4  4  3
− 
10. By what number should   be divided to give the quotient as   ?
 2   27 
36