NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Ex 13.1

These NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Ex 13.1 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Exercise 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

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

(ii) 343

343 = 7 x 7 x 7 = 7³

(iii) 729

729 = 3 x 3 x 3x 3 x 3 x 3 = 3⁶

(iv) 3125

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 or 3⁴ (ii) 5³ or 3⁵
(iii) 2⁸ or 8²
(iv) 100² or 2¹⁰⁰
(v) 2¹⁰ or 10²
Answer:
(i) 4³ or 3⁴
4³ = 4 x 4 x 4 = 64
3⁴ = 3x3x3x3 = 81
81 > 64
3⁴ > 4³
3⁴ is greater

(ii) 5³ or 3⁵
5³ = 5 x 5 x 5 = 125
3⁵ = 3x3x3x3x3 = 243
243 > 125
3⁵ > 5³
3⁵ is greater.

(iii) 2⁸ or 8²
2⁸ = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
= 256
8² = 8 x 8 = 64
256 > 64
2⁸ > 8²
2⁸ is greater.

(iv) 100² or 2¹⁰⁰
100² = 100 x 100 = 10000
2¹⁰⁰ = (2¹⁰)¹⁰
= (2x2x2x2x2x 2 x 2 x 2 x 2 x 2)¹⁰
= (1024)¹⁰ = [(1024)²]⁵
= (1024 x 1024)⁵ = (1048576)⁵
.’.(1048576) > 10000
or (1048576)⁵ > 100²
2¹⁰⁰ is greater

(v) 2¹⁰ or 10²
2¹⁰ = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 1024
10² = 10 x 10 = 100
1024 > 100
2¹⁰ > 10²
2¹⁰ is greater.

Question 5.
Express each of the following as product of powers of their prime factors.
(i) 648
(ii) 405
(iii) 540
(iv) 3600
Ans:
(i) 648

648 = 2 x 2 x 3 x 3 x 3 x 3
= 2³ x 3⁴

(ii) 405

405 = 3 x 3 x 3 x 3 x 5 = 3⁴ x 5

(iii) 540

540 = 2 x 2 x 3 x 3 x 3 x 5
= 2² x 3³ x 5

(iv) 3600

3600 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5
= 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) 5²x 3³
(vii) 2⁴ x 3²
Answer:
(i) 2 x 10³ = 2 x 10 x 10 x 10 = 2000
(ii) 7² x 2² = 7 x 7 x 2 x 2 = 49 x 4 = 196
(iii) 2³ x 5 = 2 x 2 x 2 x 5 = 8 x 5 = 40
(iv) 3 x 4⁴ = 3 x 4 x 4 x 4 x 4 = 3 x 256 = 768
(v) 0 x 10² = 0 x 10 x 10 = 0
(vi) 5² x 3³ = 5 x 5 x 3 x 3 x 3 = 25 x 27 = 675
(vii) 2⁴ x 3² = 2 x 2 x 2 x 2 x 3 x 3 = 16 x 9 = 144
(viii) 3² x 10⁴ = 3 x 3 x 10 x 10 x 10 x 10 = 9 x 10000 = 90000

Question 7.
Simplify:
(i) (-4)³
(ii) (-3) x (-2)³
(iii) (- 3)² x (- 5)²
(iv) (-2)³ x (- 10)³
Answer:
(i) (-4)³ = (-4) x (-4) x (-4) = – 64
(ii) (-3) x (-2)³ = (- 3) x (- 2) x (- 2) x (- 2) = (- 3) x (- 8) = 24
(iii) (- 3)² x (- 5)² = (-3) x (-3) x (- 5) x (- 5) = 9 x 25 = 225
(iv) (-2)³ x (- 10)³ = (- 2) x (- 2) x (- 2) x (-10) x (-10) x (- 10) =
(- 8) x (- 1000) = 8000

Question 8.
Compare the following numbers:
(i) 2.7 x 10¹²; 1.5 x 10⁸
(ii) 4 x 10¹⁴ ; 3 x 10¹⁷
Answer:
(i) 2.7 x 10¹² = \(\frac{27}{10}\) x 10¹²
= 27 x 10¹¹
(It contains 13 digits) (\(\) = a^m-n)
1.5 x 10⁸ = \(\frac{15}{10}\) x 10⁸
= 15 x 10⁷ (\(\) = a^m-n)
(It contains 9 digits)
27 x 10¹¹ > 15 x 10⁷
.’. 2.7 x 10¹² > 1.5 x 10⁸
2.7 x 10¹² is greater.

(ii) 4 x 10¹⁴ It contains 15 digits
3 x 10¹⁷ It contain 18 digits
.-. 3 x 10¹⁷ > 4 x 10¹⁴
3 x 10¹⁷ is greater.