Simplify: (i) ((2⁵)² × 7³) / (8³ × 7)   (ii) (25 × 5² × t⁸) / (10³ × t⁴)
(iii) (3⁵ ×10⁵ × 25) / (5⁷ × 6⁵)

Solution:

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

(i) ((2⁵)² × 7³) / (8³ × 7)

= (2^{5 × 2} × 7³) / ((2³)³ × 7) [(a^m)ⁿ = a^mn]

= (2¹⁰ × 7^{3 - 1}) / 2⁹ [a^m ÷ aⁿ = a^{m - n}]

= 2¹ × 7²

= 98

(ii) (25 × 5² × t⁸) / (10³ × t⁴)

= (25 × 5² × t⁸) / ((2 × 5)³ × t⁴)

= ((5)^{2 + 2} × t⁸) / (2³ × 5³ × t⁴) [a^m × aⁿ = a^{m + n}]

= (5⁴ × t⁸) / (2³ × 5³ × t⁴)

= (5^{4 - 3} × t^{8 - 4}) / 8 [a^m ÷ aⁿ = a^{m - n}]

= (5 × t ⁴) / 8

(iii) (3⁵ × 10⁵ × 25) / (5⁷ × 6⁵)

= (3⁵ × (2 × 5)⁵ × (5 × 5)) / (5⁷ × (2 × 3)⁵)

= (3⁵ × 2⁵ × 5⁵ × 5²) / (5⁷ × 2⁵ × 3⁵)

= (3⁵ × 2⁵ × 5⁷) / (5⁷ × 2⁵ × 3⁵) [a^m × aⁿ = a^{m + n}]

= 5^{7 - 7} × 2^{5 - 5} × 3^{5 - 5} [a^m ÷ aⁿ = a^{m - n}]

= 3⁰ × 2⁰× 7⁰

= 1 [a⁰ = 1]

☛ Check: NCERT Solutions for Class 7 Maths Chapter 13

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Video Solution:

Simplify: (i) ((2⁵)² × 7³) / (8³ × 7) (ii) (25 × 5² × t⁸) / (10³ × t⁴) (iii) (3⁵ ×10⁵ × 25) / (5⁷ × 6⁵)

Maths NCERT Solutions Class 7 Chapter 13 Exercise 13.2 Question 5

Summary:

We have simplified the following: (i) ((2⁵)² × 7³) / (8³ × 7) (ii) (25 × 5² × t⁸) / (10³ × t ⁴) (iii) (3⁵ ×10⁵ × 25) / (5⁷ × 6⁵) as follows (i) 98 , (ii) (5 × t⁴)/8 , (iii) 1.

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