Question

Rewrite in simplest radical form x 5/6 x 1/6

Answer 1

Answer:

$x^{\frac{5}{6}}/x^{\frac{1}{6}} = \sqrt[3]{x^2}$

Step-by-step explanation:

Given

$x^{\frac{5}{6}}/x^{\frac{1}{6}}$

Required

Rewrite in simplest radical form

Using laws of indices:

$a^m/a^n = a^{m-n}$

This implies that

$x^{\frac{5}{6}}/x^{\frac{1}{6}} = x^{\frac{5}{6} - \frac{1}{6}}$

Solve Exponents

$x^{\frac{5}{6}}/x^{\frac{1}{6}} = x^{\frac{5 - 1}{6} }$

$x^{\frac{5}{6}}/x^{\frac{1}{6}} = x^{\frac{4}{6} }$

Simplify exponent to lowest fraction

$x^{\frac{5}{6}}/x^{\frac{1}{6}} = x^{\frac{2}{3} }$

Using laws of indices:

$a^{\frac{m}{n}} = \sqrt[n]{a^m}$

This implies that

$x^{\frac{5}{6}}/x^{\frac{1}{6}} = \sqrt[3]{x^2}$

This is as far as the expression can be simplified