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

= 3⁶ × 2⁰ = 3⁶ × 1   ...[∵ a⁰ = 1]

= 729