SAT math practice question: Exponent equations

 
Try the following SAT math practice question (Calculator Permitted) that tests your understanding of algebraically manipulating exponent expressions.

Question(Calculator Permitted):

$$ (\sqrt{27})^{m} = \sqrt[3]{(81)^{n}} $$
If $m$ and $n$ are positive numbers in the equation above, what is the value of $\displaystyle \frac{m}{n}$ ?

1. $\quad \displaystyle \frac{3}{4}$
2. $\quad \displaystyle \frac{8}{9}$
3. $\quad \displaystyle \frac{9}{8}$
4. $\quad \displaystyle \frac{4}{3}$