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Answer:
![\frac{\sqrt[4]{3x^2}}{2y}](https://img.qammunity.org/2021/formulas/mathematics/high-school/qkz8hkolm2exvmditynorbc1qws9civu4b.png)
Explanation:
Fourth powers (and multiples of 4th powers) can be factored out from under the radical. Everything else remains under the radical.
![\sqrt[4]{(24x^6y)/(128x^4y^5)}=\left((3\cdot8)/(16\cdot8)x^(6-4)y^(1-5)\right)^(1/4)=(3\cdot2^(-4)x^(2)y^(-4))^(1/4)\\\\=\boxed{\frac{\sqrt[4]{3x^2}}{2y}}](https://img.qammunity.org/2021/formulas/mathematics/high-school/ztn2td5prppnjpbrsijw4d7twv2hkqi6lt.png)
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The applicable rules of exponents are ...
a^(b/c) = c-th root of (a^b)
(a^b)(a^c) = a^(b+c)
(a^b)^c = a^(bc)
a^-b = 1/a^b