$\displaystyle 3 root (x ^2 y ^ 5) ^ 12$ how do i write that as a single radical expression?
Actually, I got something different when I subtracted your exponents:
$\displaystyle \frac{8}{15}-\frac{1}{3}=\frac{1}{5}$
$\displaystyle \frac{7}{15}-\frac{-1}{5}=\frac{2}{3}$
$\displaystyle \dfrac{x^{\frac{8}{15}}y^{\frac{7}{15}}}{x^{\frac{ 1}{3}}y^{-\frac{1}{5}}}=x^{\frac{1}{3}}y^{\frac{2}{3}}$