Question

rewrite the expression with rational exponents.
\\(\sqrt7{x^{3}}\\)

\\(\sqrt7{x^{3}} = \square\\)

Explanation:

Step1: Recall the radical to exponent rule

The rule for converting a radical to a rational exponent is $\sqrt[n]{a^m}=a^{\frac{m}{n}}$. Here, we have the 7th root of $x^3$, so $n = 7$ and $m = 3$, and $a=x$.

Step2: Apply the rule

Applying the rule $\sqrt[n]{a^m}=a^{\frac{m}{n}}$ to $\sqrt[7]{x^3}$, we substitute $n = 7$, $m = 3$, and $a = x$. So we get $x^{\frac{3}{7}}$.

Answer:

$x^{\frac{3}{7}}$