Simplify (x^(2/3)y)/(x^(2/3)y^(1/3))

$\frac{x^{\frac{2}{3}} y}{x^{\frac{2}{3}} y^{\frac{1}{3}}}$

Move $y^{\frac{1}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$\frac{x^{\frac{2}{3}} y \cdot y^{- \frac{1}{3}}}{x^{\frac{2}{3}}}$

Multiply $y$ by $y^{- \frac{1}{3}}$ by adding the exponents.

Move $y^{- \frac{1}{3}}$ .

$\frac{x^{\frac{2}{3}} (y^{- \frac{1}{3}} y)}{x^{\frac{2}{3}}}$

Multiply $y^{- \frac{1}{3}}$ by $y$ .

Raise $y$ to the power of $1$ .

$\frac{x^{\frac{2}{3}} (y^{- \frac{1}{3}} y^{1})}{x^{\frac{2}{3}}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x^{\frac{2}{3}} y^{- \frac{1}{3} + 1}}{x^{\frac{2}{3}}}$

Write $1$ as a fraction with a common denominator.

$\frac{x^{\frac{2}{3}} y^{- \frac{1}{3} + \frac{3}{3}}}{x^{\frac{2}{3}}}$

Combine the numerators over the common denominator.

$\frac{x^{\frac{2}{3}} y^{\frac{- 1 + 3}{3}}}{x^{\frac{2}{3}}}$

Add $- 1$ and $3$ .

$\frac{x^{\frac{2}{3}} y^{\frac{2}{3}}}{x^{\frac{2}{3}}}$

Cancel the common factor.

$\frac{x^{\frac{2}{3}} y^{\frac{2}{3}}}{x^{\frac{2}{3}}}$

Divide $y^{\frac{2}{3}}$ by $1$ .

$y^{\frac{2}{3}}$