The expression you provided is:

$\frac{64}{49}$

and you need to simplify the cube root of this fraction.

To simplify $\sqrt[3]{\frac{64}{49}}$, we can break it down into two separate cube roots:

[ \frac{\sqrt[3]{64}}{\sqrt[3]{49}} ]

Step 1: Simplifying the numerator

The cube root of 64 is:

\sqrt[3]{64} = 4 \quad \text{(since 4^3 = 64)}

Step 2: Simplifying the denominator

The cube root of 49 is:

$\sqrt[3]{49} = 49^{1/3}$

Since 49 is not a perfect cube, we leave it as $49^{1/3}$ for the simplest form.

Thus, the simplified expression is:

$\frac{4}{49^{1/3}}$

This is the simplest form for this expression.

Would you like more details or have any questions? Here are some related questions:

1. How do you simplify square roots of fractions?
2. What is the cube root of a perfect square?
3. How do you convert radical expressions to exponents?
4. What are some other cube roots of small numbers?
5. Can cube roots be simplified the same way as square roots?

Tip: When simplifying cube roots, break the expression into separate radicals for the numerator and denominator.