Answer
$$(\frac{3xy^{3}}{5x^{-3}y^{-4}})^{2}=\frac{9}{25}x^{8}y^{14} $$
Work Step by Step
$$(\frac{3xy^{3}}{5x^{-3}y^{-4}})^{2}$$
Recall the quotient rule: $\frac{a^{m}}{a^{n}}=a^{m-n}$ and $\frac{a^{n}}{a^{m}}=\frac{1}{a^{m-n}}$
Thus,
$$(\frac{3xy^{3}}{5x^{-3}y^{-4}})^{2}$$
$$(\frac{3}{5}x^{1-(-3)}y^{3-(-4)})^{2}$$
$$(\frac{3}{5}x^{4}y^{7})^{2}$$
Recall product to power rule: $(ab)^n$ =$a^{m}b^{n}$ and power rule: $(a^{m})^{n}=a^{mn}$
Thus,
$$(\frac{3}{5}x^{4}y^{7})^{2}$$ $$(\frac{3}{5})^2x^{4(2)}y^{7(2)} $$ $$(\frac{3}{5})^2x^{8}y^{14} $$ $$\frac{9}{25}x^{8}y^{14} $$
