Rewrite $\left(\frac{17}{18}\right)^{15}$ as $\left(\frac{17}{18}\right)^{11}\times \left(\frac{17}{18}\right)^{4}$. Cancel out $\left(\frac{17}{18}\right)^{11}$ in both numerator and denominator.
$$\frac{1}{\left(\frac{17}{18}\right)^{4}}$$
Calculate $\frac{17}{18}$ to the power of $4$ and get $\frac{83521}{104976}$.
$$\frac{1}{\frac{83521}{104976}}$$
Divide $1$ by $\frac{83521}{104976}$ by multiplying $1$ by the reciprocal of $\frac{83521}{104976}$.
$$1\times \frac{104976}{83521}$$
Multiply $1$ and $\frac{104976}{83521}$ to get $\frac{104976}{83521}$.
