RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Mathematics

Created by: Abhishek Kapoor

Class 8 : RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev

The document RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev is a part of the Class 8 Course RD Sharma Solutions for Class 8 Mathematics.
All you need of Class 8 at this link: Class 8

 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) RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev
(iv)RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev12-5
(v)RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev

Answer 1: We know that an =
RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev Therefore,

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev

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

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev

Answer 2:

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

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev

= 7/12


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

(30+41)×22 

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev

=5/4 ×4 

= 5

(iii) We know from the property of powers that for every natural number aa−1 = 1/a.
Moreover, a0 is 1 for every natural number a not equal to 0. Then:
(31+41+51)=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 aa−1 = 1/a. Then: 

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev

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

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

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev

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

Answer 3:

(i) 

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev

(ii) 

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev 14-2=11/22+11/32+11/42        --> (an = 1/(an)) RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev  --> ((a/b)n = (an/bn)) 

= 4+9+16
=29 

(iii)
(2−1×4−1)÷2−2= RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev--> (an = 1/(an)) 

=1/8×418×4

= 2

(iv)
(5−1×2−1)÷6−1= RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev --> (a−n = 1/(an))

= 1/10 × 6

= 3/5

Question 4: Simplify:
(i) (41×31)24-1×3-12
(ii) (51÷61)35-1÷6-13
(iii) (21+31)12-1+3-1-1
(iv) 
(31×41)1×51

Answer 4: (i)
RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev    ---> (a−1 = 1/a)
RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev                         

(ii)
RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev  ---> (a−1 = 1/a)
RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev                            

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

(iii)
(21+31)1 =(12+13)1(2-1+3-1)-1 =12+13-1   ---> (a−1 = 1/a)
=  (56)156-1
=RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev  ---> (a−1 = 1/a)
=6/5=65

(iv)
RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev   ---> (a−1 = 1/a)
RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev 
12/5       ---> (a−1 = 1/a) 

Question 5: Simplify:

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev

Answer 5:

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev

(ii)
RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev      ---> (a−1=1/(an))
RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev         ---> ((a/b)n = (an)/(bn)) 

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev

135/8

(iii)
RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev            --->(a-n = 1/(an))
(278)÷64(27-8)÷64

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev

= 19/64

(iv)
(22+3242)÷(32)2=(4+916)× 9/4   ---> ((a/b)n = (an)/(bn)) 

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev

= -27/4

Question 6: By what number should 5−1 be multiplied so that the product may be equal to (−7)−1?

Answer 6: Using the property a−1 = 1/a for every natural number a, we have 5−1 = 1/5 and (−7)−1 = −1/7. We have to find a number x such that
1/5 ×x-1/7
Multiplying both sides by 5, we get:
x-5/7
Hence, the required number is −5/7. 

Question 7: By what number should RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev be multiplied so that the product may be equal to RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev ? 

Answer 7: Using the property a−1 = 1/a for every natural number a, we have (1/2)−1 = 2 and (−4/7)−1 = −7/4. We have to find a number x such that  

2x= -7/4

Dividing both sides by 2, we get:
x=-7/8

Hence, the required number is −7/8. 

Question 8: By what number should (−15)−1 be divided so that the quotient may be equal to (−5)−1?

Answer 8: Using the property a−1 = 1/a for every natural number a, we have (−15)−1 = −1/15 and (−5)−1 = −1/5. We have to find a number x such that

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev

or x = 1/3

Hence, (−15)−1 should be divided by 1/313 to obtain (−5)−1. 

Question 9: Write each of the following in exponential form:
(i) (3/2)1×(3/2)1×(3/2)1×(3/2)132-1×32-1×32-1×32-1
(ii) (2/5)2×(2/5)2×(2/5)225-2×25-2×25-2

Answer 9:

(i) (3/2)−1×(3/2)−1×(3/2)−1×(3/2)−1=(3/2)−1+(−1)+(−1)+(−1)                {am×an=am+n
=(3/2)−4 
(ii) (2/5)−2×(2/5)−2×(2/5)−2=(2/5)−2+(−2)+(−2)                {am×an=am+n
=(2/5)−6 

Question 10Evaluate:
(i) 5−2
(ii) (−3)−2
(iii) 
(1/3)413-4
(iv) 
(- 1/2)1

Answer 10:

 RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev         ---> (an = 1/(an)) 

= 1/25

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev      ---> (an = 1/(an)) 

= 1/9

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev  ---> (an = 1/(an)) 

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev 

= 81

(iv) RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev    ---> (a−1 = 1/(a)) 

= -2

Question 11: Express each of the following as a rational number in the form p/q:pq:

(i) 6−1
(ii) (−7)−1 

(iii) (1/4)114-1

(iv) (-4) -1 × (-3/2) -1

(v) (3/5) -1  ×( 5/2) -1

Answer 11:

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev ---> (a−1 = 1/a) 

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev  ---> (a−1 = 1/a) 

-1/7

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev ---> (a−1 = 1/a) 

= 4

(iv) RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev ---> (a−1 = 1/a) 

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev

= 1/6

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev  ---> (a−1 = 1/a) 

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev

= 2/3

Question 12: Simplify:

(i) {41×31}24-1×3-12
(ii) {51÷61}35-1÷6-13
(iii) (21+31)12-1+3-1-1
(iv) {31×41}1×513-1×4-1-1×5-1
(v) (4151)÷31 

Answer 12:

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev   ---> (a−1 = 1/a) 

= (1/12) 2   

=(1)2/(12)2                --->((a/b)n = (an)/(bn))   

= 1/144

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev  ---> (a−1 = 1/a) 

 = ( 6/5) 3

= 216/125  --->((a/b)n = (an)/(bn)) 

(iii) (21 + 31)1 = RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev−−−> (a1= 1/a) 

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev −−−> (a1= 1/a) 

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev    ---> (a−1 = 1/a) 

 =(1/12)1  × 1/5

=12×1/5   ---> (a−1 = 1/a) 

12/5

RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev ---> (a−1 = 1/a) 

  RD Sharma Solutions - Chapter 2 - Powers (Ex-2.1) - Class 8 Math Class 8 Notes | EduRev                                              

 =1/20 ×3=120×3

= 3/20

Question 13: Express each of the following rational numbers with a negative exponent:

(i) (1/4)3143

(ii) 3535
(iii) (3/5)