which is equivalent to $16^{\frac{3}{4}x}$?\n$sqrt4{16^{3x}}$\n$sqrt4x{16^{3}}$\n$sqrt3{16^{4x}}$\n$sqrt3x{16…

Explanation:

Step1: Recall exponent - radical conversion rule

The rule is $a^{\frac{m}{n}}=\sqrt[n]{a^{m}}$. In the expression $16^{\frac{3}{4}x}$, we can rewrite it as $(16^{\frac{3}{4}})^x$. First, consider $a = 16$, $m = 3$, and $n = 4$. According to the rule $a^{\frac{m}{n}}=\sqrt[n]{a^{m}}$, $16^{\frac{3}{4}}=\sqrt[4]{16^{3}}$. Then $(16^{\frac{3}{4}})^x=(\sqrt[4]{16^{3}})^x=\sqrt[4]{16^{3x}}$.

Answer:

$\sqrt[4]{16^{3x}}$ (corresponding to the first option)