Answer
$x^9y^{12}$
Work Step by Step
RECALL:
(i) The quotients-to-powers rule states that: $(\frac{a}{b})^n=\frac{a^n}{b^n}$
(ii) The power-rule states that $(a^m)^n=a^{mn}$
(iii) The negative-exponent rule states that: $a^{-m}=\dfrac{1}{a^m}$ and $\dfrac{1}{a^{-m}} = a^m$
Use the quotients-to-powers rule to find:
$=\dfrac{(x^3)^3}{(y^{-4})^3}$
Use the power rule to find:
$\\=\dfrac{x^{3(3)}}{y^{-4(3)}}
\\=\dfrac{x^{9}}{y^{-12}}$
Use the negative-exponent rule to find:
$=\dfrac{x^9}{\frac{1}{y^{12}}}
\\=x^9 \cdot \frac{y^{12}}{1}
\\=x^9y^{12}$
