which of the following is equivalent to $(5)^{\frac{7}{3}}$?\n$5^{-4}$\n$5^{4}$\n$sqrt7{5^{3}}$\n$sqrt3{5^{7}…

Answer:

D. $\sqrt[3]{5^{7}}$

Explanation:

Step1: Recall exponent - radical relationship

The rule for converting a rational - exponent to a radical is $a^{\frac{m}{n}}=\sqrt[n]{a^{m}}$, where $a$ is the base, $m$ is the numerator of the exponent, and $n$ is the denominator of the exponent.

Step2: Apply the rule to the given expression

For the expression $5^{\frac{7}{3}}$, here $a = 5$, $m = 7$, and $n = 3$. By the rule $a^{\frac{m}{n}}=\sqrt[n]{a^{m}}$, we have $5^{\frac{7}{3}}=\sqrt[3]{5^{7}}$. So the equivalent expression is $\sqrt[3]{5^{7}}$.