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
(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
(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
(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
(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
(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
(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
(i) 2.7 x 1012 = $$\frac{27}{10}$$ x 1012
= 27 x 1011
(It contains 13 digits) ( = am-n)
1.5 x 108 = $$\frac{15}{10}$$ x 108
= 15 x 107 ( = am-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.

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