NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers

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

• Class 7 Maths Exponents and Powers Exercise 13.1
• Class 7 Maths Exponents and Powers Exercise 13.2
• Class 7 Maths Exponents and Powers Exercise 13.3

NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Exercise 13.1
Ex 13.1 Class 7 Maths Question 1.
Find the value of
(i) 2 ⁶
(ii) 9 ³
(iii) 11 ²
(iv) 5 ⁴
Solution:
(i) 2 ⁶ = 2 × 2 × 2 × 2 × 2 × 2 = 64
(ii) 9 ³ = 9 × 9 × 9 = 729
(iii) 11 ² = 11 × 11 = 121
(iv) 5 ⁴ = 5 × 5 × 5 × 5 = 625

Ex 13.1 Class 7 Maths Question 2.
Exress the following in exponential form:
(i) 6 × 6 × 6 × 6
(ii) t × t
(iii) b × b × b × b
(iv) 5 × 5 × 7 × 7 × 7
(v) 2 × 2 × a × a
(vi) a × a × a × c × c × c× c × d
Solution:
(i) 6 × 6 × 6 × 6 = 6 ³
(ii) t × t = t ²
(iii) b × b × b × b = b ⁴
(iv) 5 × 5× 7 × 7 × 7 = 5 ² × 7 ³ = 5 ² · 7 ³
(v) 2 × 2 × a × a = 2 ² × a ² = 2 ² · a ²
(vi) a × a ×a × c × c × c × c × d = a ³ × c ⁴ × d = a ³ · c ⁴ · d

Ex 13.1 Class 7 Maths Question 3.
Express each of the following numbers using exponential notation:
(i) 512
(ii) 343
(iii) 729
(iv) 3125
Solution:

Ex 13.1 Class 7 Maths Question 4.
Identify the greater number, wherever possible, in each of the following?
(i) 4 ³ or 3 ⁴
(ii) 5 ³ or 3 ⁵
(iii) 2 ⁸ or 8 ²
(iv) 100 ² or 2 ¹⁰⁰
(v) 2 ¹⁰ or 10 ²
Solution:
(i) 4 ³ or 3 ⁴
4 ³ = 4 × 4 × 4 = 64,
3 ⁴ = 3 × 3 × 3 × 3 = 81
Since 81 > 64
∴ 34 is greater than 43.

(ii) 5 ³ or 3 ⁵
5 ³ = 5 × 5 × 5 = 125
3 ⁵ = 3 × 3 × 3 × 3 × 3 = 243
Since 243 > 125
∴ 35 is greater than 53.

(iii) 2 ⁸ or 8 ²
2 ⁸ =2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256
8 ² = 8 × 8 = 64
Since 256 > 64
∴ 28 is greater than 28.

(iv) 100 ² or 2 ¹⁰⁰
100 ² = 100 × 100 = 10000
2 ¹⁰⁰ = 2 × 2 × 2 × … 100 times
Here 2 × 2 × 2 ×2 × 2 × 2 × 2 ×2 × 2 × 2 × 2 × 2 × 2 × 2 = 214 = 16384
Since 16384 > 10,000
∴ 2100 is greater than 1002.

(v) 2 ¹⁰ or 10 ²
2 ¹⁰ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024
10 ² = 10 × 10 = 100
Since 1024 > 100
∴ 210 is greater than 102.

Ex 13.1 Class 7 Maths Question 5.
Express each of the following as the product of powers of their prime
(i) 648
(ii) 405
(iii) 540
(iv) 3600
Solution:

Ex 13.1 Class 7 Maths Question 6.
Simplify:
(i) 2 × 10 ³
(ii) 7 ² × 2 ²
(iii) 2 ³ × 5
(iv) 3 × 4 ⁴
(v) 0 × 10 ²
(vi) 5 ² × 3 ³
(vii) 2 ⁴ × 3 ²
(viii) 3 ² × 10 ⁴
Solution:
(i) 2 × 10 ³ = 2 × 10 × 10 × 10 = = 2000
(ii) 7 ² × 2 ² = = 7 × 7 × 2 × 2 = 196
(iii) 2 ³ × 5 = 2 × 2 × 2 × 5 = 40
(iv) 3 × 4 ⁴ = 3 × 4 × 4 × 4 × 4 = 768
(v) 0 × 10 ² = 0 × 10 × 10 = = 0
(vi) 5 ² × 3 ³ = 5 × 5 × 3 × 3 × 3 = 675
(vii) 2 ⁴ × 3 ² = 2 × 2 × 2 × 2 × 3 × 3 = 144
(viii) 3 ² × 10 ⁴ = 3 × 3 × 10 × 10 × 10 × 10 = 90000

Ex 13.1 Class 7 Maths Question 7.
Simplify:
(i) (-4) ³
(ii) (-3) × (-2) ³
(iii) (-3) ² × (-5) ²
(iv) (-2) ³ × (-10) ³
Solution:
(i) (-4) ² = (-4) × (-4) × (-4) = -64 [∵ (-a) ^{odd number} = -a ^{odd number} ]
(ii) (-3) × (-2) ³ = (-3) × (-2) × (-2) × (-2)
= (-3) × (-8) = 24
(iii) (-3) ² × (-5) ² = [(-3) × (-5)] ²
= 15 ² = 225 [∵ a ^m × b ^m = (ab) ^m )
(iv) (-2) ³ × (-10) ³ = [(-2) × (-10)] ³
= 20 ² = 8000 [∵ a ^m × b ^m = (ab) ^m ]

Ex 13.1 Class 7 Maths Question 8.
Compare the following:
(i) 2.7 × 10 ¹² ; 1.5 × 10 ⁸
(ii) 4 × 10 ¹⁴ ; 3 × 10 ¹⁴
Solution:
(i) 2.7 × 10 ¹² ; 1.5 × 10 ⁸
Here, 10 ¹² > 10 ⁸
∴ 2.7 × 10 ¹² > 1.5 × 10 ⁸
(ii) 4 × 10 ¹⁴ ; 3 × 10 ¹⁷
Here, 10 ¹⁷ > 10 ¹⁴
∴ 4 × 10 ¹⁴ < 3 × 10 ¹⁷

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