NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Ex 13.2

NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Ex 13.2

• 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 13.2
Question 1.
Using laws of e×ponents, simplify and write the answer in e×ponential form:
(i) 3² × 3⁴ × 3⁸
(ii) 6¹⁵ ÷ 6¹⁰
(iii) a³ × a²
(iv) 7^x × 7²
(v) (5²)³ ÷ 5³
(vi) 2⁵ × 5⁵
(vii) a⁴ × b⁴
(viii) (3⁴)³
(ix) (2²⁰ ÷ 2¹⁵) × 2³
(x) 8^t ÷ 8²
Solution:
(i) 3² × 3⁴ × 3⁸ = 3²⁺⁴⁺⁸ = 3¹⁴ [a^m ÷ aⁿ = a^m+n]
(ii) 6¹⁵ ÷ 6¹⁰ = 6^15-10 = 6⁵ [a^m ÷ aⁿ = a^m-n]
(iii) a³ × a² = a³⁺² = a⁵ [a^m × aⁿ = a^m+n]
(iv) 7^x × 7² = 7^x+2 [a^m × aⁿ = a^m+n]
(v) (5²)³ ÷ 5³ = 5^2×3 ÷ 5³ = 5⁶ ÷ 5³ = 5^6-3 = 5³ [(a³)ⁿ = a^mn, a^m ÷ aⁿ = a^m-n]
(vi) 2⁵ × 5⁵ = (2 × 5)⁵ = 10⁵ [a^m × b^m = (ab)^m]
(vii) a⁴ × b⁴ = (ab)⁴ [a^m × b^m = (ab)⁴]
(ix) (2²⁰ ÷ 2¹⁵) × 2³ = 2^20-15 × 2³
=2⁵ × 2³ = 2⁵⁺³ = 2⁸
(x) 8^t ÷ 8² = 8^t-2 [a^m ÷ aⁿ = a^m-n]

Question 2.
Simplify and express each of the following in exponential form:
Image may be NSFW.
Clik here to view.
Solution:
Image may be NSFW.
Clik here to view.
Image may be NSFW.
Clik here to view.
Image may be NSFW.
Clik here to view.

Question 3.
Say true or false and justify your answer:
(i) 10 × 10¹¹ = 100¹¹
(ii) 2³ > 5²
(iii) 2³ × 3² = 6⁵
(iv) 3²⁰ = (1000)⁰
Solution:
(i) 10 × 10¹¹ = 10¹⁺¹¹ = 10¹²
RHS = 100¹¹ = (10²)¹¹ = 10²²
10¹² ≠ 10²²
∴ Statement is false.

(ii) 2³ > 5²
LHS = 2³ = 8
RHS = 5²2 = 25
8 < 25
∴ 2³ < 5²
Thus, the statement is false.

(iii) 2³ × 3² = 6⁵
LHS = 2³3 × 3² = 8 × 9 = 72
RHS = 6⁵ = 6 × 6 × 6 × 6 × 6 = 7776
∴ 72 ≠ 7776
∴ The statement is false.

(iv) 3⁰ = (1000)⁰
⇒ 1 = 1 True [∵ a⁰ = 1]

Question 4.
Express each of the following as a product of prime factors only in exponential form:
(i) 108 × 192
(ii) 270
(iii) 729 × 64
(iv) 768
Solution:
(i) 108 × 192 = 2 × 2 × 3 × 3 × 3 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3
=2⁸ × 3⁴
Image may be NSFW.
Clik here to view.

(iii) 729 × 64 = 3 × 3 × 3 × 3 × 3 × 3 × 2 × 2 × 2 × 2 × 2 × 2
=3⁶ × 2⁶
Image may be NSFW.
Clik here to view.

Question 5.
Simplify:
Image may be NSFW.
Clik here to view.
Solution:
Image may be NSFW.
Clik here to view.
Image may be NSFW.
Clik here to view.

Image may be NSFW.
Clik here to view.
Image may be NSFW.
Clik here to view.
Image may be NSFW.
Clik here to view.
Image may be NSFW.
Clik here to view.
Image may be NSFW.
Clik here to view.
Image may be NSFW.
Clik here to view.

NCERT SolutionsMathsScienceSocialEnglishSanskritHindiRD Sharma

The post NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Ex 13.2 appeared first on Learn CBSE.