Page 37 - ICSE Math 8

25 × ()p − 4 ()5 2 1 () p − 4
Solution: (a) = × ×
5 () − 3 × 10 × ()p − 8 ()5 − 3 10 () p − 8

m
4
( 3
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 4 4 5 × 2
1
= ()5 5 − 1 ×× () =p 4 () 5 × ()p = 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
5
0
0
0
5
= (3) × (5) × (2) = 1 × (5) × 1 { (x) = 1}
5
= (5) = 3,125
EXERCISE 2.2
1. Evaluate. −2 − 3
–2
(a) (3) (b) (–5) –4 (c)  −  1  (d)  2 

 
p  4   5 
2. Write the following in the form q .
2
5 
(a)  3  − 1 (b) ( − ) ×6 −1   −1 (c)  3  − 1 ×    − 1
 
 
 
 5     5   2 
3
3. Simplify.
–1
–1 2
–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  − 1  3  2  − 2  3  − 4  4 −2  4 −3  4 5
− 
− 
− 
(a)     (b)   ÷   (c)   ×   ÷  
  4    3   2   7   7   7 
5. Write each of the following as a rational number with negative exponent. 3
2

3 
(a) (7) 4 (b)  4  6 (c)   2  3  − 2 (d)        − 1 

 

  

 9    3       4   

6. Write each of the following as rational number with positive exponent.
 4  − 3   1  − 2  3   3  − 3  − 4 –5 3 –4
(a)   (b)     (c)     (d) (8) × (8) × (8)
 3    5     7  
7. Simplify. −1

2

4 
7 
−

(a)  3  2 × 1 × 3 () ×   − 1 (b)  3  − 2 +  2  − 2 +  1  − 2 (c)      −  1   −2 
 
 
 
 
 2  4 − 4  3   4   3   2      3   

4 

(
1 
3 
2
3
2
(d) 5 − ) ×    − 3 (e)      − 1 ×− ( 25) − 1   − 1 (f)   1  3     2 ÷   2  − 1  3
   ×

  
 3    5     3    2    3  
–1
–1
8. By what number should (3) be multiplied to get the product as (–6) ?
25