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

December 26, 2021December 26, 2021

These NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Ex 13.2 Questions and Answers are prepared by our highly skilled subject experts.

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

Question 1.
Using laws of exponents, simplify and write the answer in exponential 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
Answer:

Question 2.
Simplify and express each of the following in exponential form:

Answer:

= 2° × 3³
= 1 × 3³ = 3³
(a° = 1)

NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Ex 13.2 4

NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Ex 13.2 6

(vi) 2° + 3°+ 4° = 1 + 1 + 1 = 3 (a° = 1)
(vii) 2° x 3° × 4° = 1 × 1 × 1 = 3 (a° = 1)
(viii) (3° + 2°) × 5° = (1 + 1) × 1 = 3 (a° = 1)
= 2 × 1 = 2

(xii) (2³ x 2)² = (2³⁺¹)²
(a^m x aⁿ = a^m+n)
= (2⁴)²
= 2⁸ (a^m)ⁿ = a^mn

Question 3.
Say true or false and justify your answer:
(i) 10 × 10¹¹ = 100¹¹
(ii) 2³ > 5²
(iii) 2³ × 3² = 6⁵
(iv) 3° = (1000)°
Answer:
(i) 10 × 10¹¹ = 100¹¹
L.H.S = 10 x 10¹¹
= 10⁽¹⁺¹¹⁾= 10¹²
(a^m × aⁿ = a^m+n)
R.H.S = 100¹¹
= (10²)H= 10²²
(a^m)ⁿ = a^mn
L.H.S ≠ R.H.S.
∴ 10 × 10¹¹ ≠ 100¹¹
This statement is false.

(ii) 2³ > 5²
2³ = 2 × 2 × 2 = 8
5² = 5 × 5 = 25
8 < 25
i. e. 2³ > 5²
This statement is false.

(iii) 2³ × 3² = 6⁵
L.H.S = 2³ × 3²
= 2 × 2 × 2 × 3 × 3 = 72
R.H.S = 6⁵ = 6 × 6 × 6 × 6 × 6
= 36 × 36 × 6
= 7776
L.H.S ≠ R.H.S.
72 ≠ 7776
∴ 2³ × 3² ≠ 6⁵
This statement is false.

(iv) 3° = (1000)°
L.H.S = 3° = 1
R.H.S = (1000)°= 1
3° = (1000)°
L.H.S = R.H.S
3° = (1000)°
∴ This statement is true.

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
Answer:
(i) 108 × 192
= 2 x 2 x 3 x 3 x 3 x 2 x 2

= 2⁸ × 3⁴