Chapter R - Section R.8 - nth Roots; Rational Exponents - R.8 Assess Your Understanding - Page 79: 83

$x^{2/3}y$

We simplify: $\displaystyle \frac{(x^{2}y)^{1/3}(xy^{2})^{2/3}}{x^{2/3}y^{2/3}}=\frac{(x^{2})^{1/3}(y)^{1/3}(x)^{2/3}(y^{2})^{2/3}}{x^{2/3}y^{2/3}}=\frac{x^{2/3}y^{1/3}x^{2/3}y^{4/3}}{x^{2/3}y^{2/3}}=x^{2/3+2/3-2/3}y^{1/3+4/3-2/3}=x^{2/3}y^{3/3}=x^{2/3}y$