The problem asks you to simplify the given radicals. Here's the solution:

First part:

We are tasked to simplify:
$\sqrt[3]{64x^6}$

Step 1: Simplify the cube root of 64

Since $64 = 4^3$, we have: $\sqrt[3]{64} = 4$

Step 2: Simplify the cube root of $x^6$

Using the property $\sqrt[3]{x^a} = x^{a/3}$, we get: $\sqrt[3]{x^6} = x^{6/3} = x^2$

Final Answer for the first part:

$\sqrt[3]{64x^6} = 4x^2$

Second part:

Simplify the fourth root (not given explicitly here but should follow a similar pattern).

Clarify if you’d like me to assist further on that part.

Would you like further breakdown or details? Here are some additional follow-up questions to expand your understanding:

1. What is the general rule for simplifying roots of powers?
2. How can properties of exponents (e.g., $a^{m/n}$) help simplify radicals?
3. What happens if the radicand (inside the radical) includes both constants and variables?
4. How does $n$-th root simplification differ from basic square or cube roots?
5. How can you rewrite a radical as an exponent to solve it algebraically?

Tip: Remember that $\sqrt[n]{a^m} = a^{m/n}$ is a key property for simplifying radical expressions.