Question

What is the value of $\frac{3^4}{3^6}$?

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

Answer 1

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

This is of the form $\frac{a^m}{a^n}=a^{m-n}=\frac{1}{a^{n-m}}$, where $m<n$.

Hence, $\frac{3^4}{3^6}$
$=3^{4-6}$
$=\frac{1}{3^{6-4}}$
$=\frac{1}{3^2}$
$=\frac{1}{9}$
Alternatively, we can solve it as
$\frac{3^4}{3^6}$
$=3^{4-6}$
$=3^{-2}$
$=(3^{-1}{)}^2$
$=(\frac{1}{3}{)}^2$
$=\frac{1^2}{3^2}$
$=\frac{1}{9}$