1. The problem asks 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, $a^{\frac{m}{n}} = \left(a^{\frac{1}{n}}\right)^m$. 3. Rewrite $16^{\frac{3}{4}}$ as $\left(16^{\frac{1}{4}}\right)^3$. 4. Calculate $16^{\frac{1}{4}}$, which is the fourth root of 16. Since $16 = 2^4$, $16^{\frac{1}{4}} = 2$. 5. Now raise 2 to the power 3: $2^3 = 8$. 6. Therefore, $16^{\frac{3}{4}} = 8$. Final answer: $8$