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

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

Simplify the denominator.

Apply the product rule to $x^{\frac{1}{3}} y^{\frac{2}{3}}$ .

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

Multiply the exponents in ${(x^{\frac{1}{3}})}^{\frac{3}{2}}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Multiply the exponents in ${(y^{\frac{2}{3}})}^{\frac{3}{2}}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Move $x^{\frac{1}{2}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

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

Multiply $x$ by $x^{- \frac{1}{2}}$ by adding the exponents.

Move $x^{- \frac{1}{2}}$ .

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

Multiply $x^{- \frac{1}{2}}$ by $x$ .

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Add $- 1$ and $2$ .

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

Cancel the common factor.

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

Divide $2 x^{\frac{1}{2}}$ by $1$ .

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

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

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