Question

How do i put (5x)-5/4 in radical form

Answer 1

`\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^( n)} \qquad \qquad \sqrt[{ m}]{a^( n)}\implies a^{\frac{{ n}}{{ m}}} \\\quad \\a^{-\frac{{ n}}{{ m}}} = \cfrac{1}{a^{\frac{{ n}}{{ m}}}} \implies \cfrac{1}{\sqrt[{ m}]{a^( n)}}\qquad\qquad \cfrac{1}{\sqrt[{ m}]{a^( n)}}= \cfrac{1}{a^{\frac{{ n}}{{ m}}}}\implies a^{-\frac{{ n}}{{ m}}} \\\\ -----------------------------\\\\`


`\bf thus \\\\ (5x)^{-(5)/(4)}\implies \cfrac{1}{(5x)^{(5)/(4)}}\implies \cfrac{1}{\sqrt[4]{(5x)^5}}\implies \cfrac{1}{\sqrt[4]{5^5x^5}} \\\\ \cfrac{1}{5x\sqrt[4]{5x}}`

Answer 2

assuming you mean
`(5x)^ (-5)/(4)`

remember

`x^(-m)= (1)/(x^m)` and

`x^ (m)/(n)= \sqrt[n]{x^m}`

combining we get

`x^ (-m)/(n)= (1)/(x^(m)/(n)) = \frac{1}{ \sqrt[n]{x^m} }`
so


`(5x)^ (-5)/(6)= (1)/((5x)^(5)/(4)) = \frac{1}{ \sqrt[4]{(5x)^5} } =\frac{1}{ 5x\sqrt[4]{5x} }`