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Evaluate : (3⁴×12³×36)/(2⁵×6³)

Solution:

Given, the expression is (3⁴×12³×36)/(2⁵×6³)

We have to evaluate the expression.

12³ can be written as (2 × 6)³

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

a^m × b^m = (a×b)^m

(2 × 6)³ = 2³ × 6³

Also, 36 can be written as 6²

Now, (3⁴×12³×36)/(2⁵×6³) = (3⁴×2³×6³×6²)/(2⁵×6³)

Considering 6³×6²,

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

a^m × aⁿ = a^m+n

Here, a = 6, m = 3 and n = 2

m + n = 3 + 2 = 5

So, 6³×6² = 6⁵

(3⁴×2³×6³×6²)/(2⁵×6³) = (3⁴×2³×6⁵)/(2⁵×6³)

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

a^m ÷ aⁿ = a^m-n

Considering 2³/2⁵,

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

m - n = 3 - 5 = -2

So, 2³/2⁵ = 2⁻²

= 1/2²

= 1/4

Considering 6⁵/6³,

Here, a = 6, m = 5 and n = 3

m - n = 5 - 3 = 2

So, 6⁵/6³ = 6²

= 36

Now, (3⁴×2³×6⁵)/(2⁵×6³) = 3⁴×1/4×36

= (3⁴×36)/4

= 3⁴×9

= 81 × 9

=729

Therefore, the required value is 729.

✦ Try This: Evaluate : (2⁴×16³)/(2⁵×16³)

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

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

Summary:

On evaluating (3⁴×12³×36)/(2⁵×6³) we get 729.

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