Question

Simplify : $\frac{3\times {27}^{n+1}+9\times 3^{3n-1}}{8\times 3^{3n}-5\times {27}^n}$

Answer 1

$\frac{3\times {27}^{n+1}+9\times 3^{3n-1}}{8\times 3^{3n}-5\times {27}^n}$
$=\frac{3\times (3^3{)}^{n+1}+3^2\times 3^{3n-1}}{2^3\times 3^{3n}-5\times 3^{3n}}$
$=\frac{3^{1+3n+3}+3^{2+3n-1}}{2^3\times 3^{3n}-5\times 3^{3n}}$
$=\frac{3^{3n+4}+3^{3n+1}}{2^3\times 3^{3n}-5\times 3^{3n}}$
$=\frac{{3^{3n}(3}^4+3^1)}{{3^{3n}(2}^3-5)}$
$=\frac{81+3}{8-5}$
$=\frac{84}{3}$
$=28$