Certainly! Let's rewrite the given expression [tex]\(\frac{1}{x^{-\frac{3}{6}}}\)[/tex] in its simplest radical form step by step.
1. Simplify the exponent:
[tex]\[
\frac{3}{6} = \frac{1}{2}
\][/tex]
Therefore, the given expression can be rewritten as:
[tex]\[
\frac{1}{x^{-\frac{1}{2}}}
\][/tex]
2. Use properties of exponents to simplify:
Recall the exponent property: [tex]\(x^{-a} = \frac{1}{x^a}\)[/tex]. Using this property:
[tex]\[
x^{-\frac{1}{2}} = \frac{1}{x^{\frac{1}{2}}}
\][/tex]
Therefore:
[tex]\[
\frac{1}{x^{-\frac{1}{2}}} = x^{\frac{1}{2}}
\][/tex]
3. Rewrite the expression as a radical:
The exponent [tex]\(\frac{1}{2}\)[/tex] can be expressed as a square root. [tex]\(x^{\frac{1}{2}} = \sqrt{x}\)[/tex].
Hence, the expression [tex]\(\frac{1}{x^{-\frac{3}{6}}}\)[/tex] simplifies to:
[tex]\[
\sqrt{x}
\][/tex]
So, the simplest radical form of [tex]\(\frac{1}{x^{-\frac{3}{6}}}\)[/tex] is [tex]\(\sqrt{x}\)[/tex].
