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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!

Which expression is equivalent to cube root of 64y^3?

Learn how to solve the problem of finding the cube root of 64y^3. This problem teaches key algebraic concepts, including radicals and exponents, suitable for students in grades 8-10.

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