Certainly! Let's simplify the given expression step by step.
We start with the fraction:
[tex]\[
\frac{x^{\frac{5}{6}}}{\frac{1}{6}}
\][/tex]
When dividing by a fraction, we can multiply by its reciprocal. So, we rewrite the expression as:
[tex]\[
x^{\frac{5}{6}} \times \frac{6}{1}
\][/tex]
Simplifying further, we multiply the exponents:
[tex]\[
x^{\frac{5}{6}} \times 6 = x^{\left(\frac{5}{6} \times 6\right)}
\][/tex]
When we multiply the exponent [tex]\(\frac{5}{6}\)[/tex] by 6, we get:
[tex]\[
\frac{5}{6} \times 6 = 5
\][/tex]
So the expression simplifies to:
[tex]\[
x^{5}
\][/tex]
Hence, the simplest radical form of [tex]\(\frac{x^{\frac{5}{6}}}{\frac{1}{6}}\)[/tex] is:
[tex]\[
x^5
\][/tex]
This means that after simplifying the original expression, we have [tex]\(x^5\)[/tex].
