Answer
$\dfrac{x}{y}$
Work Step by Step
RECALL:
(1) $(a^m)^n=a^{mn}$
(2) $(ab)^m=a^mb^m$
(3) $a^{-m} = \dfrac{1}{a^m}, a \ne 0$
(4) $\dfrac{a^m}{a^n} = a^{m-n}$
(5) $a^1 = a$
Use rule (4) above to obtain:
$=\dfrac{x^2}{x} \cdot \dfrac{y^3}{y^4}
\\=x^{2-1} \cdot y^{3-4}
\\=x^1 \cdot y^{-1}$
Use rule (5) to obtain:
$\\=x \cdot y^{-1}$
Use rule (3) above to obtain:
$=x \cdot \frac{1}{y^1}
\\=x \cdot \frac{1}{y}
\\=\dfrac{x}{y}$
