Question

write \\(\sqrt5{7}\\) using rational exponents.\
\\(\bigcirc\\) a. \\(5^7\\)\
\\(\bigcirc\\) b. \\(7^5\\)\
\\(\bigcirc\\) c. \\(5^{\frac{1}{7}}\\)\
\\(\bigcirc\\) d. \\(7^{\frac{1}{5}}\\)

Explanation:

Step1: Recall the formula for radicals to exponents

The formula is $\sqrt[n]{a}=a^{\frac{1}{n}}$, where \(n\) is the index of the radical and \(a\) is the radicand.

Step2: Apply the formula to $\sqrt[5]{7}$

Here, \(n = 5\) and \(a=7\). So using the formula, $\sqrt[5]{7}=7^{\frac{1}{5}}$.

Answer:

D. \(7^{\frac{1}{5}}\)