which is equivalent to $sqrt3{8^{\frac{1}{4}x}}$?\n$8^{\frac{3}{4}x}$\n$sqrt7{8^{x}}$\n$sqrt12{8^{x}}$\n$8^{\…

Explanation:

Step1: Recall exponent - radical rule

We know that $\sqrt[n]{a^m}=a^{\frac{m}{n}}$. So, $\sqrt[3]{8^{\frac{1}{4}x}}=(8^{\frac{1}{4}x})^{\frac{1}{3}}$.

Step2: Apply power - of - a - power rule

According to the power - of - a - power rule $(a^m)^n=a^{mn}$. Here, $a = 8$, $m=\frac{1}{4}x$, and $n=\frac{1}{3}$. Then $(8^{\frac{1}{4}x})^{\frac{1}{3}}=8^{\frac{1}{4}x\times\frac{1}{3}}=8^{\frac{1}{12}x}=\sqrt[12]{8^{x}}$.

Answer:

$\sqrt[12]{8^{x}}$