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:

Solution:

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

(iii) 729 × 64 = 3 × 3 × 3 × 3 × 3 × 3 × 2 × 2 × 2 × 2 × 2 × 2
=3⁶ × 2⁶

Question 5.
Simplify:

Solution:

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