Question

Question 180(v)

Simplify

$\frac{(9{)}^3\times 27\times t^4}{(3{)}^{-2}\times (3{)}^4\times t^2}$

Answer 1

$\frac{(9{)}^3\times 27\times t^4}{(3{)}^{-2}\times (3{)}^4\times t^2}=\frac{(3^2{)}^3\times (3{)}^3\times t^4}{(3{)}^{-2}\times (3{)}^4\times t^2}[\because 3\times 3=3^2=9]$
$=\frac{(3{)}^6\times (3{)}^3\times t^4}{(3{)}^{-2}\times (3{)}^4\times t^2}$
$=(3{)}^6\times (3{)}^3\times (3{)}^2\times (3{)}^{-4}\times t^4\times t^{-2}[\because a^{-m}=\frac{1}{a^m}]$
$=(3{)}^{6+3+2+(-4)}\times t^{4+(-2)}[\because a^m\times a^n=\left(a{)}^{m+n}\right]$

$=3^{11-4}\times t^{4-2}$

$=3^7\times t^2$