Answer:
[tex]\sqrt{x}[/tex]
Step-by-step explanation:
Given expression:
[tex]\dfrac{1}{x^{-\frac36}}[/tex]
To rewrite the given expression in its simplest radical form, begin by simplifying the exponent of the term in the denominator:
[tex]-\dfrac{3}{6}=-\dfrac{3\div 3}{6\div 3}=-\dfrac{1}{2}[/tex]
Therefore:
[tex]\dfrac{1}{x^{-\frac36}}=\dfrac{1}{x^{-\frac12}}[/tex]
Now, apply the Negative Exponent Rule to the term in the denominator.
[tex]\boxed{\begin{array}{c}\underline{\textsf{Negative Exponent Rule}}\\\\a^{-m}=\dfrac{1}{a^m}\end{array}}[/tex]
Therefore:
[tex]\dfrac{1}{x^{-\frac12}}=\dfrac{1}{\left(\dfrac{1}{x^{\frac12}}\right)}[/tex]
Taking the reciprocal of 1/n results in n, so:
[tex]\dfrac{1}{\left(\dfrac{1}{x^{\frac12}}\right)}=x^{\frac12}[/tex]
When a number is raised to 1/2, it means taking the square root of that number. So, the given expression rewritten in its simplest radical form is:
[tex]\LARGE\boxed{\boxed{\sqrt{x}}}[/tex]
