Which expression is equivalent to \( 4^{\frac{7}{3}} \) ? \( (\sqrt[7]{4})^{3}-(\sqrt[3]{4})^{7} \) \( 7 \sqrt[3]{4}-3 \sqrt[7]{4} \)

To find an expression equivalent to \( 4^{\frac{7}{3}} \), it can help to rewrite \( 4 \) in a simpler form. Since \( 4 = 2^2 \), we have \( 4^{\frac{7}{3}} = (2^2)^{\frac{7}{3}} = 2^{\frac{14}{3}} \). This means we're dealing with powers and roots of \( 2 \), and any similar transformation can help confirm equivalence in expressions. Now, let's break down the contenders given: both expressions involve combinations of roots and powers of \( 4 \). You can test their equivalence by rewriting them in terms of \( 2 \) or simplifying directly. Remember to apply the properties of exponents and roots carefully, as that's the key to unveil the underlying relationship!