1. The problem asks us to simplify the expression $16^{\frac{3}{4}}$. 2. Recall the rule: the $n$-th root of a number $a$ is $a^{\frac{1}{n}}$. Therefore, $a^{\frac{m}{n}} = \left(a^{\frac{1}{n}}\right)^m = \left(\sqrt[n]{a}\right)^m$. 3. Here, $16^{\frac{3}{4}}$ means the fourth root of 16 raised to the power 3. 4. Calculate the fourth root of 16: since $16 = 2^4$, $\sqrt[4]{16} = 2$. 5. Now raise this result to the power 3: $2^3 = 8$. 6. Therefore, $16^{\frac{3}{4}} = 8$. 7. Final answer: $8$.