Answer:
[tex]\dfrac{y^{18}}{8x^{18}}[/tex]
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
a^-b = 1/a^b
(a^b)^c = a^(bc)
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Your expression simplifies as follows:
[tex]\left(\dfrac{10x^3y^{-2}}{5x^{-3}y^4}\right)^{-3}=(2x^{3-(-3)}y^{-2-4})^{-3}=(2x^6y^{-6})^{-3}\\\\=(2^{-3})x^{6(-3)}y^{(-6)(-3)}=\dfrac{1}{8}x^{-18}y^{18}\\\\=\boxed{\dfrac{y^{18}}{8x^{18}}}[/tex]
