NCERT Solutions Class 7 Mathematics Exponents and Powers Ex 13.1

Question: 1.Find the value of:

(i) 2⁶

(ii) 9³

(iii) 11²

(iv) 5⁴

Answer :
(i) 2⁶ = 2 x 2 x 2 x 2 x 2 x 2 = 64

(ii) 9³ = 9 x 9 x 9 = 729

(iii) 11² = 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 :
(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) 4³ and 3⁴

(ii) 5³ or 3⁵

(iii) 2⁸ or 8²

(iv) 100² or 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, 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, 3⁵ 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, 2⁸ is greater than 8².

(iv) 100² = 100 x 100 = 10,000

2¹⁰⁰ = 2 x 2 x 2 x 2 x 2 x …..94 times x ……… x 2 = 16,384 x ….. x 2

Since, 10,000 < 16,384 x ……. X 2

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 = 10 x 10 = 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 :
(i) 648 = 2³ x 3⁴

(ii) 405 = 5 x 3⁴

(iii) 540 = 2² x 3³ x 5

(iv) 3,600 = 2⁴ x 3² x 5²

Question: 6.Simplify:

(i) 2 x 10³

(ii) 7² x 2²

(iii) 2³ x 5

(iv) 3 x 4⁴

(v) 0 x 10²

(vi) 5² x 3³

(vii) 2⁴ x 63²

(viii) 3² x 10⁴

Answer :
(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) 5² x 3³ = 5 x 5 x 3 x 3 x 3 = 675

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

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