Question

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

• A. $28$
• B. $14$
• C. $27$
• D. none of the above

Answer 1

The correct option is A $28$

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

$=\frac{3\times (3^3{)}^{n+1}+3^2\times 3^{3n-1}}{2^3\times 3^{3n}-5\times 3^{3n}}$

$=\frac{3^{1+3n+3}+3^{2+3n-1}}{2^3\times 3^{3n}-5\times 3^{3n}}$

$=\frac{3^{3n+4}+3^{3n+1}}{2^3\times 3^{3n}-5\times 3^{3n}}$

$=\frac{{3^{3n}(3}^4+3^1)}{{3^{3n}(2}^3-5)}$

$=\frac{81+3}{8-5}$

$=\frac{84}{3}$

$=28$