Question

Simplify:

`((9)^3 xx 27 xx t^4)/((3)^-2 xx (3)^4 xx t^2)`

Answer 1

Given, `((9)^3 xx 27 xx t^4)/((3)^-2 xx (3)^4 xx t^2)`

= `((3^2)^3 xx (3)^3 xx t^4)/((3)^-2 xx (3)^4 xx t^2)`  ...[∵ 3 × 3 = 3² = 9]

= `((3)^6 xx (3)^3 xx t^4)/((3)^-2 xx (3)^4 xx t^2)`

= (3)⁶ × (3)³ × (3)² × (3)^–4 × t⁴ × t^–2  ...`[∵ a^-m = 1/a^m]`

= (3)^{11 – 4} × t^{4 – 2}  ...[∵ a^m × aⁿ = (a)^{m – n}]

= (3)⁷ × t²