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

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

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

Explanation:

Step1: Recall the rule of fractional exponents

The rule (a^{\frac{m}{n}}=\sqrt[n]{a^{m}}) (where (a > 0), (m,n\in\mathbb{Z}), (n> 1)). For the expression (5^{\frac{7}{3}}), here (a = 5), (m = 7), (n=3).

Step2: Apply the rule

By the rule (a^{\frac{m}{n}}=\sqrt[n]{a^{m}}), when (a = 5), (m = 7), (n = 3), we get (5^{\frac{7}{3}}=\sqrt[3]{5^{7}}).

Answer:

(\sqrt[3]{5^{7}}) (the fourth option)