Question

Find the value of $\frac{3^{12+n}\times 9^{2n-7}}{3^{5n}}$

• A. $\frac{1}{9}$
• B. $\frac{2}{9}$
• C. $\frac{3}{9}$
• D. $\frac{4}{9}$

Answer 1

The correct option is A $\frac{1}{9}$

$\frac{3^{12+n}\times 9^{2n-7}}{3^{5n}}=\frac{3^{12+n}\times (3^2{)}^{2n-7}}{3^{5n}}=\frac{3^{12+n}\times 3^{4n-14}}{3^{5n}}=\frac{3^{12+n+4n-14}}{3^{5n}}$
$=\frac{3^{5n-2}}{3^{5n}}=3^{5n-2-5n}=3^{-2}=\frac{1}{3^2}=\frac{1}{9}$