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Evaluate (125×5²×a⁷)/(10³×a⁴)

Solution:

Given, the expression is (125 × 5² × a⁷)/(10³ × a⁴)

We have to evaluate the expression.

125 can be written as 5³

10³ can be written as (2 × 5)³

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

a^m × b^m = (a × b)^m

(2 × 5)³ = 2³ × 5³

Now, (125 × 5² × a⁷)/(10³ × a⁴) = (5³ × 5² × a⁷)/(2³ × 5³ × a⁴)

Considering 5³ × 5²,

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

a^m × aⁿ = a^{m + n}

Here, a = 5, m = 3 and n = 2

m + n = 3 + 2 = 5

So, 5³ × 5² = 5⁵

Now, (125 × 5² × a⁷)/(10³ × a⁴) = (5⁵ × a⁷)/(2³ × 5³ × a⁴)

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

a^m ÷ aⁿ = a^m-n

Considering 5⁵/5³,

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

m - n = 5 - 3 = 2

So, 5⁵/5³ = 5²

Considering a⁷/a⁴,

Here, m = 7 and n = 4

m - n = 7 - 4 = 3

So, a⁷/a⁴ = a³

(5⁵×a⁷)/(2³×5³×a⁴) = (5²×a³)/2³

= 25a³/8

Therefore, (125×5²×a⁷)/(10³×a⁴) = 25a³/8.

✦ Try This: Evaluate (100×2²×b³)/(2³×b²)

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

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

Summary:

On evaluating (125×5²×a⁷)/(10³×a⁴) we get 25a³/8.

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