Answer:
[tex]x^{\frac{5}{6}}/x^{\frac{1}{6}} = \sqrt[3]{x^2}[/tex]
Step-by-step explanation:
Given
[tex]x^{\frac{5}{6}}/x^{\frac{1}{6}}[/tex]
Required
Rewrite in simplest radical form
Using laws of indices:
[tex]a^m/a^n = a^{m-n}[/tex]
This implies that
[tex]x^{\frac{5}{6}}/x^{\frac{1}{6}} = x^{\frac{5}{6} - \frac{1}{6}}[/tex]
Solve Exponents
[tex]x^{\frac{5}{6}}/x^{\frac{1}{6}} = x^{\frac{5 - 1}{6} }[/tex]
[tex]x^{\frac{5}{6}}/x^{\frac{1}{6}} = x^{\frac{4}{6} }[/tex]
Simplify exponent to lowest fraction
[tex]x^{\frac{5}{6}}/x^{\frac{1}{6}} = x^{\frac{2}{3} }[/tex]
Using laws of indices:
[tex]a^{\frac{m}{n}} = \sqrt[n]{a^m}[/tex]
This implies that
[tex]x^{\frac{5}{6}}/x^{\frac{1}{6}} = \sqrt[3]{x^2}[/tex]
This is as far as the expression can be simplified
