Question

Simplify the following:

${\displaystyle \frac{3^n\times 9^{n+1}}{3^{n-1}\times 9^{n-1}}}$

Answer 1

${\displaystyle \frac{3^n\times 9^{n+1}}{3^{n-1}\times 9^{n-1}}}$

${\displaystyle =\frac{3^n\times {\left(3^2\right)}^{n+1}}{3^{n-1}\times {\left(3^2\right)}^{n-1}}}$

${\displaystyle =\frac{3^n\times 3^{2n+2}}{3^{n-1}\times 3^{2n-2}}}$

${\displaystyle =\frac{3^{n+2n+2}}{3^{n-1+2n-2}}}$

${\displaystyle =\frac{3^{3n+2}}{3^{3n-3}}}$

${\displaystyle =3^{3n+2-3n+3}}$

= 3⁵

= 243