rewrite in simplest radical form $\frac{x^{\frac{5}{6}}}{x^{\frac{1}{6}}}$. show each step of your process.

Explanation:

Step1: Use exponent - subtraction rule

When dividing two terms with the same base $a^m\div a^n=a^{m - n}$, here $a = x$, $m=\frac{5}{6}$, $n=\frac{1}{6}$. So $\frac{x^{\frac{5}{6}}}{x^{\frac{1}{6}}}=x^{\frac{5}{6}-\frac{1}{6}}$.

Step2: Calculate the exponent

$\frac{5}{6}-\frac{1}{6}=\frac{5 - 1}{6}=\frac{4}{6}=\frac{2}{3}$. So $x^{\frac{5}{6}-\frac{1}{6}}=x^{\frac{2}{3}}$.

Step3: Convert to radical form

The rule for converting from exponent form $a^{\frac{m}{n}}$ to radical form is $a^{\frac{m}{n}}=\sqrt[n]{a^{m}}$. Here $a = x$, $m = 2$, $n = 3$. So $x^{\frac{2}{3}}=\sqrt[3]{x^{2}}$.

Answer:

$\sqrt[3]{x^{2}}$