Algebra Examples

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

Step 1

Simplify the denominator.

Tap for more steps...

Step 1.1

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

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

Step 1.2

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

Tap for more steps...

Step 1.2.1

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

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

Step 1.2.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.2.2.1

Cancel the common factor.

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

Step 1.2.2.2

Rewrite the expression.

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

Step 1.3

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

Tap for more steps...

Step 1.3.1

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

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

Step 1.3.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.3.2.1

Cancel the common factor.

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

Step 1.3.2.2

Rewrite the expression.

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

Step 1.3.3

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.3.3.1

Cancel the common factor.

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

Step 1.3.3.2

Rewrite the expression.

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

Step 1.4

Simplify.

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

Step 2

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

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

Step 3

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

Tap for more steps...

Step 3.1

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

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

Step 3.2

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

Tap for more steps...

Step 3.2.1

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

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

Step 3.2.2

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

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

Step 3.3

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

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

Step 3.4

Combine the numerators over the common denominator.

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

Step 3.5

Add $- 1$ and $2$ .

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

Step 4

Cancel the common factor.

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

Step 5

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

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