The problem shown asks to determine which expression is equivalent to $\sqrt[3]{64y^3}$.

Let's break it down:

1. We know that $\sqrt[3]{64y^3}$ means we are looking for the cube root of both 64 and $y^3$.

2. First, find the cube root of 64: $\sqrt[3]{64} = 4$ because $4^3 = 64$.

3. Next, take the cube root of $y^3$, which is just $y$ since: $\sqrt[3]{y^3} = y$

So, $\sqrt[3]{64y^3} = 4y$.

Thus, the correct answer is $4y$.

Do you want more details or have any other questions? Here are five related questions to expand your knowledge:

1. How do you compute cube roots for non-perfect cubes?
2. What happens if the exponent in $y^3$ were different (e.g., $y^5$)?
3. How would you solve for higher roots, like $\sqrt[4]{x}$?
4. What’s the difference between cube roots and square roots?
5. Can radicals and exponents be used together, such as $(x^2)^{1/3}$?

Tip: Remember, the cube root of $x^n$ can be rewritten as $x^{n/3}$, which simplifies many expressions!