Answer
$-\frac{27y^{12}}{8x^{9}}$
Work Step by Step
Given : $(-\frac{3y^{4}}{2x^{3}}$$)^{3}$
This becomes : $(-1)^{3}\times\frac{(3y^{4})^{3}}{(2x^{3})^{3}}=$ $-1\times\frac{3^{3}\times y^{12}}{2^{3}\times x^{9}}$
(since $(\frac{a}{b}$ $)^{m}=$ $\frac{a^{m}}{b^{m}}$ and $(a^{m})^{n}=$ $a^{mn}$)
This becomes : $-\frac{27y^{12}}{8x^{9}}$
