Question

If $9^n={27}^{n+1}$, then calculate the value of $2^n$.

• A. $-\frac{10}{3}$
• B. $-\frac{8}{3}$
• C. $-\frac{3}{8}$
• D. $\frac{1}{8}$
• E. $\frac{3}{8}$

Answer 1

Answer: (D)

$\frac{1}{8}$

Given $9^n={27}^{n+1}$, which implies
$3^{2n}=3^{3n+3}$
Now compare powers, we get
$2n=3n+3$ , which implies $n=-3$
Therefore $2^n=2^{-3}=\frac{1}{8}$