Evaluate $(\sqrt[3]{13})^6$.
To evaluate this expression, I need to simplify it using the exponent rules for radicals and powers. I can rewrite the expression as $(13^{1/3})^6$, since a cube root is the same as raising to the power of $\frac{1}{3}$. Then, I can use the rule that says $(a^b)^c = a^{bc}$, which means I can multiply the exponents inside and outside the parentheses. So, I get $(13^{1/3})^6 = 13^{(1/3) \cdot 6}$. Simplifying the fraction, I get $13^{(1/3) \cdot 6} = 13^2$. Finally, I can calculate $13^2 = 169$. 