#### Answer

$= \frac{1}{256}$

#### Work Step by Step

1) We need all of the fractions to have a common denominator of $12$, so we multiply the first fraction by $4$, the second fraction by $3$ and the third fraction by $2$.
2) Remember PEDMAS. Thus, do everything in grouping symbols first and then the exponent.
$= (\frac{1}{3} - \frac{1}{4} + \frac{1}{6})^{4}$
$= (\frac{1(4)}{12} - \frac{1(3)}{12} + \frac{1(2)}{12})^{4}$
$= (\frac{4}{12} - \frac{3}{12} + \frac{2}{12})^{4}$
$= (\frac{1}{12} + \frac{2}{12})^{4}$
$= (\frac{3}{12})^{4}$
$= (\frac{1}{4})^{4}$
$= \frac{1}{256}$