Answer
$\frac{q^{11}}{t^{11}}, t\ne0$
Work Step by Step
Based on the power of a quotient rule, we know that $(\frac{a}{c})^{n}=\frac{a^{n}}{c^{n}}$ (where $n$ is a positive integer and $a$ and $c$ are real numbers).
Therefore, $(\frac{q}{t})^{11}=\frac{q^{11}}{t^{11}}, t\ne0$.