NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev

Mathematics (Maths) Class 7

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Class 7 : NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev

The document NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev is a part of the Class 7 Course Mathematics (Maths) Class 7.
All you need of Class 7 at this link: Class 7

Exercise 13.1 

Question 1: Find the value of: 

(i) 2

(ii) 9

(iii) 11

(iv) 5

Answer 1: 

(i) 26 =2x2x2x2x2x2 = 64
(ii) 93 = 9x9x9 = 729
(iii) 11= 11 x 11= 121
(iv) 54 =5 x 5 x 5 x 5 = 625


Question 2: Express the following in exponential form: 

(i) 6 x 6 x 6 x 6  
(ii) t x t
(iii) b x b x b x b  
(iv) 5 x 5 x 7 x 7 x 7
(v) 2 x 2 x a x a  
(vi) a x a x a x c x c x c x c x d

Answer 2: 

(i) 6 x 6 x 6 x 6 = 64
(ii) t x t = t2
(iii) b x b x b x b = b4
(iv) 5 x 5 x 7 x 7 x 7 = 52 x 73
(v) 2 x 2 x a x a = 2x a2
(vi) a x a x a x c x c x c x c x d = a3 x c4 x d


Question 3: Express each of the following numbers using exponential notation: 

(i) 512  
(ii) 343  
(iii) 729  
(iv) 3125

Answer 3: 

(i) 512

512 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 29

2       512

2

256

2

128

2

64

2

32

2

16

2

8

2

4

2

2

 

1

 

(ii) 343
343 = 7 x 7 x 7 = 73

7       343

7

49

7

7

 

1

 

(iii) 729 
729 = 3 x 3 x 3 x 3 x 3 x 3 = 36

3       729

3

243

3

81

3

27

3

9

3

3

 

1

 

(iv) 3125
3125 = 5 x 5 x 5 x 5 x 5

5

3125

5

625

5

125

5

25

5

5

 

1

 

Question 4: Identify the greater number, wherever possible, in each of the following: 

(i)  43 and 34 
(ii)  53 or 35
(iii) 28 or 82 
(iv) 100or 2100
(v) 210 or 102

Answer 4: 

(i) 43 = 4 x 4 x 4 = 64
34 = 3 x 3 x 3 x 3 = 81
Since 64 < 81
Thus, 34 is greater than 43.

(ii) 53 = 5 x 5 x 5 = 125
35 = 3 x 3 x 3 x 3 x 3 = 243
Since, 125 < 243
Thus, 34 is greater than 53.

(iii) 28= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256
82 = 8x8 = 64
Since, 256 > 64
Thus, 28 is greater than 82.

(iv) 1002 = 100 x 100 = 10,000
2100 = 2 x 2 x 2 x 2 x 2 x.......14 times x....x 2 = 16,384 x....x 2
Since, 10,000 < 16,384 x....x2
Thus, 2100 is greater than 1002.

(v)  210 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 1,024
102 = 10x10 = 100
Since, 1,024 > 100
Thus, 210 >102


Question 5: Express each of the following as product of powers of their prime factors: 

(i) 648 

(ii) 405 

(iii) 540 

(iv) 3,600 

Answer 5: 

(i)    648 = 23 x 34

2

648

2

324

2

162

3

81

3

27

3

9

3

3

 

1

 

(ii) 405 = 5 x 34

5

405

3

81

3

27

3

9

3

3

 

1

 

(iii) 540 = 22 x 33 x 5

2

540

2

270

3

135

3

45

3

15

5

5

 

1

 

(iv) 3,600 = 24 x 3x 52

2

3600

2

1800

2

900

2

450

3

225

3

75

5

25

5

5

1

 

Question 6: Simplify: 

(i)  2 x 103   
(ii) 72 x 22
(iii) 23 x 5  
(iv) 3 x 44
(v) 0 x 102 
(vi) 5x 33
(vii) 24 x 32 
(viii) 32 x 104

Answer 6: 

(i)  2 x 103  = 2 x 10 x 10 x 10  = 2,000
(ii)  72 x 22 = 7 x 7 x 2 x 2  = 196
(iii) 23 x 5 = 2 x 2 x 2 x 5  = 40
(iv) 3 x 44 = 3 x 4 x 4 x 4 x 4  = 768
(v) 0 x 102 = 0 x 10 x 10  = 0
(vi) 53 x 33 = 5 x 5 x 3 x 3 x 3  = 675
(vii) 2x 32  = 2 x 2 x 2 x 2 x 3 x 3  = 144
(viii) 32 x 104 = 3 x 3x 10x10x 10x10  =  90,000


Question 7: Simplify: 

(i) (-4)3   
(ii) (-3)x(-2)3
(iii) (-3)x (-5)2   
(iv) (-2)3 x (-10)3

Answer 7:

(i)  (-4)3 = (-4)x(-4)x(-4) = -64
(ii) (-3)x(-2)3 =(-3)x(-2)x(-2)x(-2) = 24
(iii) (-3)2 x (-5)2 = (-3)x(-3)x(-5) x (-5) = 225
(iv) (-2)3x(-10)3 =(-2)x(-2)x(-2)x(-10)x(-10)x(-10)


Question 8: Compare the following numbers: 

(i) 2.7 x 1012; 1.5 x 108 

(ii) 4 x 1014; 3 x 1017 

Answer 8: 

(i) 2.7 x 1012 and 1.5 x 108
On comparing the exponents of base 10,
2.7 x 1012 > 1.5x108

(ii) 4 x 1014 and 3 x 1017
On comparing the exponents of base 10,
4 x 1014 < 3 x 1017


Exercise 13.2 

Question 1: Using laws of exponents, simplify and write the answer in exponential form: 

(i) 32 x 34 x 38   
(ii) 615 ÷ 610
(iii) a3 x a   
(iv) 7x x 72
(v) (52)2 ÷ 53   
(vi) 25 x 55
(vii) a4 x b4
(viii) (34)3
(ix) [220 ÷ 215) x 23

(x) 8t x 82

Answer 1: 

(i) NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev       NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
(ii)  NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev            NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
(iii)  NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev             NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
(iv)  NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev                       NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
(v)  NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRevNCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev                                      NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
(vi) NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev      NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
(vii) NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev            NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
(viii)  NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev            NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
(ix)  NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRevNCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev                NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
(x)  NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev                    NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev


Question 2: Simplify and express each of the following in exponential form: 

(i) NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
(ii) NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
(iii)  NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
(iv)  NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
(v)  NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
(vi) NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
(vii)  NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
(viii)  NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
(ix)  NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
(x)  NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
(xi) NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
(xii)  NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev

 

Answer 2: 

(i) NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev                 NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev                                           NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev

(ii) NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev                      NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev                                         NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRevNCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev

(iii) NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev                          NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRevNCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev

(iv) NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev     NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev

(v)    NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev                                               NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev                                                          NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev

(vi) NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev                                       NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev

(vii) NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev                                      NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev

(viii) NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev                     NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev

(ix) NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev                         NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev                                          NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev                                                             NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
(x)  NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev            NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev                                                     NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev

(xi) NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRevNCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev

NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev                                                   NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev

(xii) NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev                        NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev

Question 3: Say true or false and justify your answer: 

(i) 10 x 1011 = 10011   
 (ii)  23 > 52
 (iii) 23x 32 = 6s    
 (iv) 30 = (1000)0

Answer 3: 

(i) 10x1011 = 10011
L.H.S. 101+11 = 1012    and R.H.S. (102)11=1022
Since, L.H.S. ≠ R.H.S.
Therefore, it is false.

(ii) 23 > 52
L.H.S 23 = 8    and R.H.S. 52 = 25
Since, L.H,S. is not greater than R.H.S.
Therefore, it is false,

(iii) 23 x32 = 65
L.H.S. 23 x 32 = 8 x 9 = 72    and R.H.S. 65 =7.776
Since, L.H.S. ≠ R.H.S.
Therefore, it is false.

(iv) 3° = (1000)°
L.H.S. 3° = 1    and R.H.S. (1000)° = 1
Since, L.H.S. = R.H.S.
Therefore, it is true.


Question 4: Express each of the following as a product of prime factors only in exponential form:
(i) 108 x 192
(ii) 270
(iii) 729 x 64
(iv) 768
Answer 4: 
NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev

 NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev

NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev


Question 5: Simplify: 

(i) NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
(ii)  NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
(iii) NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev

Answer 5:

(i) 
NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev

(ii) 
NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev

(iii) 
NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev
NCERT Solutions(Part - 1) - Exponents and Powers Class 7 Notes | EduRev

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