Chapter 2 - Powers (Ex-2.1) - Class 8 Math RD Sharma Solutions | RD Sharma Solutions for Class 8 Mathematics PDF Download

 Question 1: Express each of the following as a rational number of the form p/q,pq, where p and q are integers and q ≠ 0.

(i) 2⁻³
(ii) (−4)⁻² 

(iii) 
(iv)12-5
(v)

Answer 1: We know that a−n =
 Therefore,

Question 2: Fiind the value of each of the following:
(i) 3⁻¹ + 4⁻¹
(ii) (3⁰ + 4⁻¹) × 2²
(iii) (3⁻¹ + 4⁻¹ + 5⁻¹)⁰

Answer 2:

(i) We know from the property of powers that for every natural number a, a⁻¹ = 1/a. Then:

= 7/12

(ii) We know from the property of powers that for every natural number a, a⁻¹ = 1/a.
Moreover, a⁰ is 1 for every natural number a not equal to 0. Then: 

(30+4−1)×22 

=5/4 ×4 

= 5

(iii) We know from the property of powers that for every natural number a, a⁻¹ = 1/a.
Moreover, a⁰ is 1 for every natural number a not equal to 0. Then:
(3−1+4−1+5−1)=1(3-1+4-1+5-1)=1          ---> (Ignore the expression inside the bracket and use a⁰ = 1 immediately.) 

(iv) We know from the property of powers that for every natural number a, a⁻¹ = 1/a. Then: 

 =−1-1                       ---> (a⁻¹ = 1/a) 

Question 3:Find the value of each of the following:

(iii) (2⁻¹ × 4⁻¹) ÷ 2⁻²
(iv) (5⁻¹ × 2⁻¹) ÷ 6⁻¹ 

Answer 3:

(i) 

(ii) 

 14-2=11/22+11/32+11/42        --> (a⁻ⁿ = 1/(aⁿ))   --> ((a/b)ⁿ = (aⁿ/bⁿ)) 

= 4+9+16
=29 

(iii)
(2−1×4−1)÷2−2= --> (a⁻ⁿ = 1/(aⁿ)) 

=1/8×418×4

= 2

(iv)
(5−1×2−1)÷6−1=  --> (a−n = 1/(an))

= 1/10 × 6

= 3/5

Question 4: Simplify:
(i) (4−1×3−1)24-1×3-12
(ii) (5−1÷6−1)35-1÷6-13
(iii) (2−1+3−1)−12-1+3-1-1
(iv) (3−1×4−1)−1×5−1

Answer 4: (i)
    ---> (a⁻¹ = 1/a)
                         

(ii)
  ---> (a−1 = 1/a)
                            

=  (6/5)³
=  (6)³ /(5)³   ---> ((a/b)n = (an)/(bn) )
= 216/125

(iii)
(2−1+3−1)−1 =(12+13)−1(2-1+3-1)-1 =12+13-1   ---> (a⁻¹ = 1/a)
=  (56)−156-1
=  ---> (a⁻¹ = 1/a)
=6/5=65

(iv)
   ---> (a⁻¹ = 1/a)
 
= 12/5       ---> (a⁻¹ = 1/a) 

Question 5: Simplify:

Answer 5:

(ii)
      ---> (a⁻¹=1/(aⁿ))
         ---> ((a/b)ⁿ = (aⁿ)/(bⁿ)) 

= 135/8

(iii)
            --->(a^-n = 1/(aⁿ))
= (27−8)÷64(27-8)÷64

= 19/64

(iv)
(22+32−42)÷(32)2=(4+9−16)× 9/4   ---> ((a/b)ⁿ = (aⁿ)/(bⁿ)) 

= -27/4