Answer:
[tex]\displaystyle\frac{\sqrt[4]{3x^2}}{2y}[/tex]
Step-by-step explanation:
It can work well to identify 4th powers under the radical, then remove them.
[tex]\displaystyle\sqrt[4]{\frac{24x^6y}{128x^4y^5}}=\sqrt[4]{\frac{3x^2}{16y^4}}=\sqrt[4]{\frac{3x^2}{(2y)^4}}\\\\=\frac{\sqrt[4]{3x^2}}{2y}[/tex]
_____
The applicable rules of exponents are ...
1/a^b = a^-b
(a^b)(a^c) = a^(b+c)
The x-factors simplify as ...
x^6/x^4 = x^(6-4) = x^2
The y-factors simplify as ...
y/y^5 = 1/y^(5-1) = 1/y^4
The constant factors simplify in the usual way:
24/128 = (8·3)/(8·16) = 3/16
