Simplify (x^(4/3)y^(2/3))/((xy)^(1/3))

$\frac{x^{\frac{4}{3}} y^{\frac{2}{3}}}{{(x y)}^{\frac{1}{3}}}$

Step 1

Apply the product rule to $x y$ .

$\frac{x^{\frac{4}{3}} y^{\frac{2}{3}}}{x^{\frac{1}{3}} y^{\frac{1}{3}}}$

Step 2

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

$\frac{x^{\frac{4}{3}} y^{\frac{2}{3}} x^{- \frac{1}{3}}}{y^{\frac{1}{3}}}$

Step 3

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

$x^{\frac{4}{3}} y^{\frac{2}{3}} x^{- \frac{1}{3}} y^{- \frac{1}{3}}$

Step 4

Multiply $x^{\frac{4}{3}}$ by $x^{- \frac{1}{3}}$ by adding the exponents.

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

$x^{- \frac{1}{3}} x^{\frac{4}{3}} y^{\frac{2}{3}} y^{- \frac{1}{3}}$

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

$x^{- \frac{1}{3} + \frac{4}{3}} y^{\frac{2}{3}} y^{- \frac{1}{3}}$

Combine the numerators over the common denominator.

$x^{\frac{- 1 + 4}{3}} y^{\frac{2}{3}} y^{- \frac{1}{3}}$

Add $- 1$ and $4$ .

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

Divide $3$ by $3$ .

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

Step 5

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

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

Step 6

Multiply $y^{\frac{2}{3}}$ by $y^{- \frac{1}{3}}$ by adding the exponents.

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

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

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

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

Combine the numerators over the common denominator.

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

Add $- 1$ and $2$ .

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