A day full of math games & activities. Find one near you.

Evaluate : (6⁴×9²×25³)/(3²×4²×15⁶)

Solution:

Given, the expression is (6⁴×9²×25³)/(3²×4²×15⁶)

We have to evaluate the expression.

6⁴ can be written as (2 × 3)⁴

9² can be written as (3 × 3)²

25³ can be written as (5 × 5)³

4² can be written as (2 × 2)²

15⁶ can be written as (3 × 5)⁶

Now, (6⁴×9²×25³) = (2 × 3)⁴ × (3 × 3)² × (5 × 5)³

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

a^m × b^m = (a×b)^m

= 2⁴ × 3⁴ × 3² × 3² × 5³ × 5³

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

a^m × aⁿ = a^m+n

= 2⁴ × 3^{4 + 2 + 2} × 5^{3 + 3}

= 2⁴ × 3⁸ × 5⁶

Similarly, 3²×4²×15⁶ = 3²×(2×2)²×(3 × 5)⁶

= 3² × 2² × 2² × 3⁶ × 5⁶

= 3^{2 + 6} × 2^{2 + 2} × 5⁶

= 3⁸ × 2⁴ × 5⁶

Now, (6⁴×9²×25³)/(3²×4²×15⁶) = (2⁴ × 3⁸ × 5⁶)/(3⁸ × 2⁴ × 5⁶)

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

a^m ÷ aⁿ = a^m-n

Considering 2⁴/2⁴,

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

m - n = 4 - 4 = 0

2⁴/2⁴ = 2⁰

We know a⁰ = 1

So, 2⁰ = 1

Similarly, 3⁸/3⁸ = 1

5⁶/5⁶ = 1

Now, (2⁴ × 3⁸ × 5⁶)/(3⁸ × 2⁴ × 5⁶) = 1 × 1 × 1

= 1

Therefore, the required value is 1.

✦ Try This: Evaluate : (5⁴×9²×81³)/(5²×3²×81)

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

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

Summary:

On evaluating the expression (6⁴×9²×25³)/(3²×4²×15⁶) we get 1

☛ Related Questions: