Simplify and express each of the following in exponential form:
(i) (2³ × 3³ × 4) / (3 × 32)   (ii) ((5² )³ × 5⁴) ÷ 5⁷   (iii) 25⁴ ÷ 5³
(iv) (3 × 7² ×11⁸) / (21×11³)   (v) 3⁷ / (3⁴ × 3³)   (vi) 2⁰ + 3⁰ + 4⁰
(vii) 2⁰ × 3⁰ × 4⁰   (viii) (3⁰ + 2⁰ )× 5⁰   (ix) (2⁸ × a⁵) / (4³ × a³)
(x) (a⁵ / a³) × a⁸   (xi) (4⁵ × a⁸b³) / (4⁵ × a⁵b²)   (xii) (2³ × 2)²

Solution:

To solve this question, we be using the laws of exponents.

(i) (2³ × 3⁴ × 4) / (3 × 32)

= (2³ × 3⁴ × 2²) / (3 × 2⁵)

= (2^{3 +  2} × 3⁴) / (3¹ × 2⁵) [a^m × aⁿ = a^{m + n}]

= (2⁵ × 3^{4 - 1}) / (2⁵) [a^m ÷ aⁿ = a^{m - n}]

= 3³

(ii) ((5² )³ × 5⁴) ÷ 5⁷

= [5⁶ × 5⁴] ÷ 5⁷ [(a^m)ⁿ = a^mn]

= 5^{6 + 4} ÷ 5⁷ [a^m × aⁿ = a^{m + n}]

= 5¹⁰ ÷ 5⁷

= 5^{10 - 7} [a^m ÷ aⁿ = a^{m - n}]

= 5³

(iii) 25⁴ ÷ 5³

= (5²)⁴ ÷ 5³

= 5⁸ ÷ 5³ [(a^m)ⁿ = a^mn]

= 5^{8 - 3} [a^m ÷ aⁿ = a^{m - n}]

= 5⁵

(iv) (3 × 7² × 11⁸) / (21 × 11³)

= (3 × 7² × 11⁸) / (3 × 7 × 11³) [Since, 21 = 3 × 7]

= (7² × 11⁸) / (7 × 11³)

= 7^{2 - 1} × 11^{8 - 3} [a^m ÷ aⁿ = a^{m - n}]

= 7 × 11⁵

(v) 3⁷ / (3⁴ × 3³)

= 3⁷ / 3^{4 + 3} [a^m × aⁿ = a^{m + n}]

= 3⁷ / 3⁷

= 3^{7 - 7} [am ÷ an = am-n]

= 3⁰

= 1 [a^o = 1]

(vi) 2⁰ + 3⁰ + 4⁰

= 1 + 1 + 1 [a^o = 1]

= 3

(vii) 2⁰ × 3⁰ × 4⁰

= 1 × 1 × 1 [a^o = 1]

= 1

(viii) (3⁰ + 2⁰ ) × 5⁰

= (1 + 1) × 1 [a^o = 1]

= 2 × 1

= 2

(ix) (2⁸ × a⁵) / (4³ × a³)

= (2⁸ × a⁵) / ((2²)³ × a³)

= (2⁸ × a⁵) / (2⁶ × a³) [(a^m)ⁿ = a^mn]

= 2^{8 - 6} × a^{5 - 3} [a^m ÷ aⁿ = a^{m - n}]

= 2² × a²

(x) (a⁵ / a³) × a⁸

= a^{5 - 3} × a⁸ [a^m ÷ aⁿ = a^{m - n}]

= a² × a⁸

= a^{2 + 8} [a^m × aⁿ = a^{m + n}]

= a¹⁰

(xi) (4⁵ × a⁸b³) / (4⁵ × a⁵b²)

= 4^{5 - 5} × a^{8 - 5} × b^{3 - 2} [a^m ÷ aⁿ = a^{m - n}]

= 4⁰ × a³ × b

= a³ × b [a^o = 1]

(xii) (2³ × 2)²

= (2^3 + 1)² [a^m × aⁿ = a^{m + n}]

= (2⁴)²

= 2^{4 × 2} [(a^m)ⁿ = a^mn]

= 2⁸

☛ Check: NCERT Solutions for Class 7 Maths Chapter 13

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Video Solution:

Simplify and express each of the following in exponential form: (i) (2³ × 3³ × 4) / (3×32) (ii) [(5² )³ × 5⁴] ÷ 5⁷ (iii) 25⁴ ÷ 5³ (iv) (3 × 7² ×11⁸) / (21×11³) (v) 3⁷ / (3⁴ × 3³) (vi) 2⁰ + 3⁰ + 4⁰(vii) 2⁰ × 3⁰ × 4⁰ (viii) (3⁰ + 2⁰ )× 5⁰ (ix) (2⁸ × a⁵) / (4³ × a³) (x) (a⁵ / a³) × a⁸ (xi) (4⁵ × a⁸b³) / (4⁵ × a⁵b²) (xii) (2³ × 2)²

Maths NCERT Solutions Class 7 Chapter 13 Exercise 13.2 Question 2

Summary:

We have simplified and expressed each of the following in exponential form: (i) (2³ × 3³ × 4) / (3×32) (ii) [(5² )³ × 5⁴] ÷ 5⁷ (iii) 25⁴ ÷ 5³ (iv) (3 × 7² ×11⁸) / (21×11³) (v) 3⁷ / (3⁴ × 3³) (vi) 2⁰ + 3⁰ + 4⁰(vii) 2⁰ × 3⁰ × 4⁰ (viii) (3⁰ + 2⁰ )× 5⁰ (ix) (2⁸ × a⁵) / (4³ × a³) (x) (a⁵ / a³) × a⁸ (xi) (4⁵ × a⁸b³) / (4⁵ × a⁵b²) (xii) (2³ × 2)² as follows: (i) 3³ , (ii) 5³ , (iii) 5⁵ , (iv) 7 × 11⁵ , (v) 1 , (vi) 3 , (vii) 1 , (viii) 2, (ix) 2² × a², (x) a¹⁰ , (xi) a³ × b, (xii) 2⁸.

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