CBSE students can refer to NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers InText Questions and Answers are provided by experts in order to help students secure good marks in exams.
Class 7 Maths NCERT Solutions Chapter 13 Exponents and Powers InText Questions
Try These (Page 250)
Question 1.
Write 172, 5642, and 6374 in an expanded form.
Solution:
172 = 1 × 100 + 7 × 10 + 2
= 1 × 102 + 7 × 10 + 2
5642 = 5 × 1000 + 6 × 100 + 4 × 10 + 2
= 5 × 103 + 6 × 102 + 4 × 10 + 2
6374 = 6 × 1000 + 3 × 100 + 7 × 10 + 4
= 6 × 103 + 3 × 102 + 7 × 10 + 4
Try These (Page 250)
Question 1.
Find five more such examples, where a number is expressed in exponential form. Also, identify the base and the exponent in each case.
Solution:
(i) 34 = 3 × 3 × 3 × 3 = 81
In 34, 3 is known as base and 4 as an exponent.
(ii) 44 = 4 × 4 × 4 × 4 = 256
In 44, 4 is known as base and 4 as an exponent.
(iii) 75 = 7 × 7 × 7 × 7 × 7 = 16807
In 75, 7 is known as base and 5 as an exponent.
(iv) 53 = 5 × 5 × 5 = 125
In 53, 5 is known as base and 3 as an exponent.
(v) 26 = 2 × 2 × 2 × 2 × 2 × 2 = 64
In 26,2 is known as base and 6 as an exponent.
Try These (Page 251)
Question 1.
(i) 729 as a power of 3
Solution:
We have
∴ 729 = 3 × 3 × 3 × 3 × 3 × 3 = 36
(ii) 128 as a power of 2
Solution:
We have
∴ 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 27
(iii) 343 as a power of 7.
Solution:
(iii) We have
∴ 343 = 7 × 7 × 7 = 73
Try These (Page 254)
Question 1.
Simplify and write in exponential form :
(i) 25 × 23
Solution:
25 × 23 = 25 + 3 = 28
(ii) p3 x p2
Solution:
p3 × p2 = p3 + 2 = p5
(iii) 43 × 42
Solution:
43 × 42 = 43 + 2 = 45
(iv) a3 × a2 × a7
Solution:
a3 × a2 × a7 = a3+2+7 = a12
(v) 53 × 57 × 512
Solution:
53 × 57 × 512 = 53+7+12 = 522
(vi) (- 4)100 × (- 4)20
Solution:
(- 4)100 × (- 4)20 = (- 4)100+20 = (- 4)120
Try These (Page 255)
Question 1.
Simplify and write in exponential form : (e.g.,116 ÷ 112 = 114)
(i) 29 ÷ 23
Solution:
29 ÷ 23 = 29-3 = 26
(ii) 108 ÷ 104
Solution:
108 ÷ 104 = 108-4 =104
(iii) 911 ÷ 97
Solution:
911 ÷ 97 = 911-7 = 94
(iv) 2015 ÷ 2013
Solution:
2015 ÷ 2013 = 2015-13 = 202
(v) 713 ÷ 710
Solution:
713 ÷ 710 = 713-10 = 73
Try These (Page 255)
Question 1.
Simplify and write the answer in exponential form:
(i) (62)4
Solution:
(62)4 = 62×4 = 68
(ii) (22)100
Solution:
(22)100 = 22×100 = 2200
(iii) (750)2
Solution:
(750)2 = 750×2 = 7100
(iv) (53)7
Solution:
(53)7 = 53×7 = 521
Try These (Page 256)
Question 1.
Put into another form using am × bm = (ab)m :
(i) 43 × 23
Solution:
43 × 23 = (4 × 4 × 4) × (2 × 2 × 2)
= (4 × 2) × (4 × 2) × (4 × 2)
= (4 × 2)3
(ii) 25 × 65
Solution:
25 × 65 = (2 × 2 × 2 × 2 × 2) × (b × b × b × b × b)
= (2 × b) × (2 × b) × (2 × b) × (2 × b) × (2 × b)
= (2 × b)5 = (2b)5
(iii) a2 × t2
Solution:
a2 × t2 = (a × a) × (t × t) = (a × t) × (a × t)
=(a × t)2 = (at)2
(iv) 56 × (- 2)6
Solution:
56 × (- 2)6 = (5 × 5 × 5 × 5 × 5 × 5 ) × (- 2 × – 2 × – 2 × – 2 × – 2 × – 2)
= (5 × – 2) × (5 × – 2) × (5 × – 2) × (5 × – 2) × (5 × – 2) × (5 × – 2)
= (5 × – 2)6
(v) (-2)4 × (-3)4
Solution:
(- 2)4 × (- 3)4 = (- 2 × – 2 × – 2 × – 2) × (- 3 × – 3 × – 3 × – 3)
= (- 2 × – 3) × (- 2 × – 3) × (- 2 × – 3) × (- 2 × – 3)
= (- 2 × – 3)4
Try These (Page 257)
Put into another form using
(i)
Solution:
(ii)
Solution:
(iii)
Solution:
(iv)
Solution:
(v)
Solution:
Try These (Page 261)
Question 1.
Expand by expressing powers of 10 in the exponential form :
(i) 172
Solution:
172 = 1 × 100 + 7 × 10 + 2 × 1
= 1 × 102 + 7 × 101 + 2 × 10°
(ii) 5,643
Solution:
5643 = 5 × 1000 + 6 × 100 + 4 × 10 +3 × 1
= 5 × 103 + 6 × 102 + 4 × 101 + 3 x 10°
(iii) 56,439
Solution:
56439 = 5 × 10000 + 6 × 1000 + 4 × 100 + 3 × 10 + 9
= 5 × 104 + 6 × 103 +4 × 102 + 3 × 101 + 9 × 10°
(iv) 1,76,428
Solution:
176428 = 1 × 100000 + 7 × 10000 + 6 × 1000 + 4 × 100 + 2 × 10 + 8 × 1
= 1 × 105 + 7 × 104 + 6 × 103 + 4 × 102 + 2 × 101 + 8 × 10°
Try These (Page 262)
Question 1.
The distance between Sun and Saturn is 1,433,500,000,000 m or 1.4335 × 1012 m. The distance between Saturn and Uranus is 1,439,000,000,000 m or 1.439 × 1012 m. The distance between Sun and Earth is 149,600,000,000 m or 1.496 × 1011 m. Can you tell which of the three distances is the smallest?
Solution:
Of the three given distances, the distance between Sun and Earth is the smallest.