Question

Rewrite in simplest radical form 1/x^-3/6

Answer 1

$\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad \sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}} \\\quad \\ % rational negative exponent a^{-\frac{{ n}}{{ m}}} = \cfrac{1}{a^{\frac{{ n}}{{ m}}}} \implies \cfrac{1}{\sqrt[{ m}]{a^{ n}}} \\ \quad \\ \quad \\ % radical denominator \cfrac{1}{\sqrt[{ m}]{a^{ n}}}= \cfrac{1}{a^{\frac{{ n}}{{ m}}}}\implies a^{-\frac{{ n}}{{ m}}}\qquad thus\\ ----------------------------\\ \\ \quad$$\bf \\ \quad \\ \cfrac{1}{x^{-\frac{3}{6}}}\implies \cfrac{1}{x^{-\frac{1}{2}}}\implies \cfrac{1}{\frac{1}{x\frac{1}{2}}}\implies \cfrac{1}{1}\cdot \cfrac{x^{\frac{1}{2}}}{1} \\ \quad \\ x^{\frac{1}{2}}\implies \sqrt{x}$