# How do you write (6x^(1/2))/(15x^(2/3)) in radical form?

$\frac{6}{15 \sqrt[6]{x}}$.
By application of the laws of exponents and surds which state that ${x}^{\frac{m}{n}} = \sqrt[n]{{x}^{m}}$, as well as the laws of exponents stating $\frac{{x}^{m}}{{x}^{n}} = {x}^{m - n} \mathmr{and} {x}^{- n} = \frac{1}{{x}^{n}}$,
$\frac{6}{15} {x}^{\frac{1}{2} - \frac{2}{3}} = \frac{6}{15} {x}^{- \frac{1}{6}} = \frac{6}{15 {x}^{\frac{1}{6}}} = \frac{6}{15 \sqrt[6]{x}}$.