Question

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

Answer 1

`x^{(5)/(6)}/x^{(1)/(6)} = \sqrt[3]{x^2}`

Explanation:

Given

`x^{(5)/(6)}/x^{(1)/(6)}`

Required

Rewrite in simplest radical form

Using laws of indices:

`a^m/a^n = a^(m-n)`

This implies that

`x^{(5)/(6)}/x^{(1)/(6)} = x^{(5)/(6) - (1)/(6)}`

Solve Exponents

`x^{(5)/(6)}/x^{(1)/(6)} = x^{(5 - 1)/(6) }`

`x^{(5)/(6)}/x^{(1)/(6)} = x^{(4)/(6) }`

Simplify exponent to lowest fraction

`x^{(5)/(6)}/x^{(1)/(6)} = x^{(2)/(3) }`

Using laws of indices:

`a^{(m)/(n)} = \sqrt[n]{a^m}`

This implies that

`x^{(5)/(6)}/x^{(1)/(6)} = \sqrt[3]{x^2}`

This is as far as the expression can be simplified