Answer:
The answer is [tex]\sqrt{x}[/tex]
Step-by-step explanation:
Step 1: Deal with the negative exponent applying this rule:
[tex]x^{-b} = \frac{1}{x^{b}}[/tex]
In this case
[tex]b=- \frac{3}{6}[/tex]
Putting all together:
[tex]\frac{1}{x^{-\frac{3}{6}}} =x^{-(-\frac{3}{6}) } =x^{\frac{3}{6}}[/tex]
Step 2: Reduce the fractional exponent
The fractional exponent [tex]\frac{3}{6}[/tex] can be reduced dividing the numerator and denominator of the fraction by the least common multiple.
In order to find it, we have
[tex]3=(3)*(1)\\6=(3)*(2)\\[/tex]
Therefore, the least common multiple is 3
Reducing the fraction:
[tex]\frac{3}{6}=\frac{3\div3}{6\div3}=\frac{1}{2}[/tex]
Therefore:
[tex]x^{\frac{3}{6}}=x^{\frac{1}{2}}[/tex]
Step 3: Deal with the fractional exponent
A fractional exponent can be expressed as a root, following this rule:
[tex]x^{ \frac{a}{b}} = \sqrt[b]{x^{a}}[/tex]
In this case:
[tex]a=1\\b=2[/tex]
As the index of the root is 2, this is a square root, therefore:
[tex]x^{\frac{1}{2}} = \sqrt{x}[/tex]
