The problem asks to simplify the expression $\sqrt[4]{p^4 q^8}$. We assume that $p$ and $q$ represent any real numbers.

1. Problem Description

The problem asks to simplify the expression $\sqrt[4]{p^4 q^8}$. We assume that $p$ and $q$ represent any real numbers.

2. Solution Steps

We are asked to simplify the expression $\sqrt[4]{p^4 q^8}$.

We can rewrite the expression using fractional exponents:

$\sqrt[4]{p^4 q^8} = (p^4 q^8)^{\frac{1}{4}}$

Using the power of a product rule, we have:

$(p^4 q^8)^{\frac{1}{4}} = (p^4)^{\frac{1}{4}} (q^8)^{\frac{1}{4}}$

Using the power of a power rule, we have:

$(p^4)^{\frac{1}{4}} (q^8)^{\frac{1}{4}} = p^{4 \cdot \frac{1}{4}} q^{8 \cdot \frac{1}{4}} = p^1 q^2 = p q^2$

3. Final Answer

$pq^2$