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Evaluate : (5⁴×7⁴×2⁷)/(8×49×5³)

Solution:

Given, the expression is (5⁴ × 7⁴ × 2⁷)/(8 × 49 × 5³)

We have to evaluate the expression.

8 can be written as 2³

49 can be written as 7²

So, (8 × 49 × 5³) = (2³ × 7² × 5³)

Now, (5⁴ × 7⁴ × 2⁷)/(8 × 49 × 5³) = (5⁴ × 7⁴ × 2⁷)/(2³ × 7² × 5³)

(5⁴ × 7⁴ × 2⁷)/(2³ × 7² × 5³) can be written as (5⁴/5³) × (7⁴/7²) × (2⁷/2³)

For any non-zero integers ‘a’ and ‘b’ and whole numbers m and n,

a^m ÷ aⁿ = a^{m - n}

Considering 5⁴/5³,

Here, a = 5, m = 4 and n = 3

m - n = 4 - 3 = 1

So, 5⁴/5³ = 5¹ = 5

Considering 7⁴/7²,

Here, a = 7, m = 4 and n = 2

m - n = 4 - 2 = 2

7⁴/7² = 7²

= 7 × 7

7⁴/7² = 49

Considering 2⁷/2³,

Here, a = 2, m = 7 and n = 3

m - n = 7 - 3 = 4

2⁷/2³ = 2⁴

= 2 × 2 × 2 × 2

= 4 × 4

2⁷/2³ = 16

Now, (5⁴/5³) × (7⁴/7²) × (2⁷/2³) = 5 × 49 × 16

= 3920

Therefore, (5⁴ × 7⁴ × 2⁷)/(8 × 49 × 5³) = 3920.

✦ Try This: Evaluate : (6² × 3⁴ × 2³)/(6 × 8 × 27)

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 13

NCERT Exemplar Class 7 Maths Chapter 11 Problem 85 (b)

Summary:

On evaluating (5⁴×7⁴×2⁷)/(8×49×5³) we get 3920.

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