Question

Evaluate:

`(3^4 xx 12^3 xx 36)/(2^5 xx 6^3)`

Answer 1

We have, `(3^4 xx 12^3 xx 36)/(2^5 xx 6^3) = (3^4 xx (2^2 xx 3)^3 xx (2^2 xx 3^2))/(2^5 xx (2 xx 3)^3`  ......[∵ 12 = 2 × 2 × 3 and 36 = 2 × 2 × 3 × 3]

= `(3^4 xx 2^6 xx 3^3 xx 2^2 xx 3^2)/(2^5 xx 2^3 xx 3^3)` ......[∵ (a × b)^m = a^m × b^m]

= `((3^4 xx 3^2 xx 3^3) xx (2^6 xx 2^2))/((2^5 xx 2^3) xx 3^3)`  

= `(3^(4+2+3) xx 2^(6+2))/(2^(5+3) xx 3^3)`  ......[∵ a^m × aⁿ = a^m+n]

= `(3^9 xx 2^8)/(3^3 xx 2^8)` = 3^9–3 × 2^8–8  ......`[∵ a^m/a^n = a^(m-n)]`

= 3⁶ × 2⁰ = 3⁶ × 1   ......[∵ a⁰ = 1]

= 729