Answer:
![\displaystyle\frac{\sqrt[4]{3x^2}}{2y}](https://img.qammunity.org/2020/formulas/mathematics/high-school/ek4v7c3q0tgtr6p45joejrkftafkdeeaem.png)
Explanation:
It can work well to identify 4th powers under the radical, then remove them.
![\displaystyle\sqrt[4]{(24x^6y)/(128x^4y^5)}=\sqrt[4]{(3x^2)/(16y^4)}=\sqrt[4]{(3x^2)/((2y)^4)}\\\\=\frac{\sqrt[4]{3x^2}}{2y}](https://img.qammunity.org/2020/formulas/mathematics/high-school/bnb81j4bgp4u95l55yxcx13pqs3axgn5fz.png)
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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