Question

Rewrite in simplest radical form x^ 5/6 over x^ 1/6 show each step of your process

Answer 1

Answer:  $\bold{\sqrt[3]{x^2} }$

Step-by-step explanation:

$\dfrac{x^{\frac{5}{6}}}{x^{\frac{1}{6}}}\\\\\\=x^{\frac{5}{6}-\frac{1}{6}}}}\\\\\\=x^{\frac{4}{6}}}}\\\\\\=x^{\frac{2}{3}}}}\\\\=\sqrt[3]{x^2}$

Answer 2

Answer:

The simplest Radical = $\sqrt{x^{3} }$

Step-by-step explanation:

The two terms of the fraction are $x^{\frac{5}{6}}$⇒numerator

and $x^{\frac{1}{6}}$⇒denominator

Both of them are same variable x

So we can use the rule of the power:

If we divide to terms have the same base we subtract their powers

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

If the power is in the shape of fraction so the numerator of the fraction represents the radical and the denominator represents the power inside the radical.

$x^{\frac{2}{3} }=\sqrt{x^{3} }$