We want to simplify the expression
[tex]\frac{1}{x^{(-\frac{3}{6})}}[/tex]First we will simplify the exponent:
[tex]-\frac{3}{6}\rightarrow-\frac{1}{2}[/tex]So now we have
[tex]\frac{1}{x^{(-\frac{1}{2})}}[/tex]Next, we need to apply the negative exponent property, which states that for any positive value of m and n,
[tex]\frac{1}{m^{-n}}\rightarrow m^n[/tex](We flip the fraction to the its reciprocal, then change the sign of the exponent.)
Our new expression is:
[tex]x^{\frac{1}{2}}[/tex]Finally, we need to apply the rational exponent rule. Which states for any positive integer value of m and n,
[tex]x^{\frac{m}{n}}=\sqrt[n]{x^m}[/tex]Notice the n becomes the index of the radical, and the m becomes the power of the number under the radical.
So, we have
[tex]\sqrt[2]{x}^1\rightarrow\sqrt{x}[/tex]Our final answer is
[tex]\boxed{\sqrt{x}}[/tex]