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^{-(3)/(6)}}\implies \cfrac{1}{x^{-(1)/(2)}}\implies \cfrac{1}{(1)/(x(1)/(2))}\implies \cfrac{1}{1}\cdot \cfrac{x^{(1)/(2)}}{1} \\ \quad \\ x^{(1)/(2)}\implies √(x)`