The question is given to be:
[tex]\frac{x^{\frac{5}{6}}}{x^{\frac{1}{6}}}[/tex]
Recall the exponent rule given to be:
[tex]\frac{a^m}{a^n}=a^{m-n}[/tex]
Therefore, we can simplify the expression to be:
[tex]\frac{x^{\frac{5}{6}}}{x^{\frac{1}{6}}}=x^{\frac{5}{6}-\frac{1}{6}}[/tex]
Simplifying the exponent, we have:
[tex]x^{\frac{5}{6}-\frac{1}{6}}=x^{\frac{4}{6}}=x^{\frac{2}{3}}[/tex]
To write in radical form, apply the rule given to be:
[tex]a^{\frac{m}{m}}=(\sqrt[n]{a}^{})^m[/tex]
Therefore, the answer becomes:
[tex]\Rightarrow(\sqrt[3]{x})^2[/tex]
ANSWER
[tex]\frac{x^{\frac{5}{6}}}{x^{\frac{1}{6}}}=(\sqrt[3]{x})^2[/tex]
