Question

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

Answer 1

assuming you mean $(5x)^ \frac{-5}{4}$

remember
$x^{-m}= \frac{1}{x^m}$ and
$x^ \frac{m}{n}= \sqrt[n]{x^m}$

combining we get
$x^ \frac{-m}{n}= \frac{1}{x^\frac{m}{n}} = \frac{1}{ \sqrt[n]{x^m} }$
so

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

Answer 2

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

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