Rewrite $\left(\frac{11}{12}\right)^{6}$ as $\left(\frac{11}{12}\right)^{4}\times \left(\frac{11}{12}\right)^{2}$. Cancel out $\left(\frac{11}{12}\right)^{4}$ in both numerator and denominator.
$$\frac{1}{\left(\frac{11}{12}\right)^{2}}$$
Calculate $\frac{11}{12}$ to the power of $2$ and get $\frac{121}{144}$.
$$\frac{1}{\frac{121}{144}}$$
Divide $1$ by $\frac{121}{144}$ by multiplying $1$ by the reciprocal of $\frac{121}{144}$.
$$1\times \frac{144}{121}$$
Multiply $1$ and $\frac{144}{121}$ to get $\frac{144}{121}$.
