Exponents and Powersv - Solutions

 CBSE Class –VII Mathematics

NCERT Solutions
Chapter 13 Exponents and Powers
 (Ex. 13.1)


Question 1. Find the value of:

(i) 26     (ii)93     (iii)112   (iv) 54

Answer: (i) 2= 2 x 2 x 2 x 2 x 2 x 2 = 64

(ii) 9= 9 x 9 x 9 = 729

(iii) 11= 11 x 11 = 121

(iv) 5= 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: (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 = 22 x 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: (i) 512 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 29
(ii) 343 = 7 x 7 x 7 = 73
(iii) 729 = 3 x 3 x 3 x 3 x 3 x 3 = 36
(iv) 3125 = 5 x 5 x 5 x 5 x 5 = 55

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

(i) 4or 34

(ii) 5or 35

(iii) 2or 82

(iv) 100or 2100

(v) 210 or 102

Answer: (i) 43= 4 x 4 x 4 = 64

34= 3 x 3 x 3 x 3 = 81

Since 64 < 81

Thus, 3is 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= 8 x 8 = 64

Since, 256 > 64

Thus, 28is greater than82.

(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 ……. X 2

Thus, 2100is greater than1002.

(v) 210= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 1,024

102= 10 x 10 = 100

Since, 1,024 > 100

Thus, 210102

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: (i) 648 = 23×34

(ii) 405 = 5×34

(iii) 540 = 22×33×5

(iv) 3,600 = 24×32×52

Question 6. Simplify:

(i) 2×103

(ii) 72×22

(iii)23×5

(iv) 3×44

(v)0×102

(vi) 52×33

(vii)24×632

(viii) 32×104

Answer: (i) 2×103= 2 x 10 x 10 x 10 = 2,000

(ii) 72×22= 7 x 7 x 2 x 2 = 196

(iii) 23×5= 2 x 2 x 2 x 5 = 40

(iv) 3×44= 3 x 4 x 4 x 4 x 4 = 768

(v) 0×102= 0 x 10 x 10 = 0

(vi) 52×33= 5 x 5 x 3 x 3 x 3 = 675

(vii) 24×632= 2 x 2 x 2 x 2 x 3 x 3 = 144

(viii) 32×104= 3 x 3 x 10 x 10 x 10 x 10 = 90,000

Question 7. Simplify:

(i) (-4)3

(ii) (3)×(2)3

(iii) (3)2×(5)2

(iv) (2)3×(10)3

Answer: (i) (4)3=(4)×(4)×(4)=64

(ii) (3)×(2)3=(3)×(2)×(2)×(2)=24

(iii) (3)2×(5)2=(3)×(3)×(5)×(5)=225

(iv) (2)3×(10)3=(2)×(2)×(2)×(10)×(10)×(10)=8000

Question 8. Compare the following numbers:

(i) 2.7×1012;1.5 x 108

(ii) 4×10143×1017

Answer: (i) 2.7×1012and 1.5 x 108

On comparing the exponents of base 10,

2.7×10121.5 x 108

(ii) 4×1014and 3×1017

On comparing the exponents of base 10,

4×1014