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Answer:
[tex]\dfrac{\sqrt[4]{3x^2}}{2y}[/tex]
Step-by-step explanation:
Fourth powers (and multiples of 4th powers) can be factored out from under the radical. Everything else remains under the radical.
[tex]\sqrt[4]{\dfrac{24x^6y}{128x^4y^5}}=\left(\dfrac{3\cdot8}{16\cdot8}x^{6-4}y^{1-5}\right)^{1/4}=(3\cdot2^{-4}x^{2}y^{-4})^{1/4}\\\\=\boxed{\dfrac{\sqrt[4]{3x^2}}{2y}}[/tex]
_____
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
