Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Cancel the common factor of $3$ .

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Step 2.2.1

Cancel the common factor.

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

Step 2.2.2

Rewrite the expression.

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

Step 3

Simplify.

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

Step 4

Rewrite $x^{2} y^{2}$ as ${(x y)}^{2}$ .

$x y^{3} \sqrt{{(x y)}^{2}}$

Step 5

Pull terms out from under the radical, assuming positive real numbers.

$x y^{3} (x y)$

Step 6

Multiply $x$ by $x$ by adding the exponents.

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Step 6.1

Move $x$ .

$x \cdot x y^{3} y$

Step 6.2

Multiply $x$ by $x$ .

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

Step 7

Multiply $y^{3}$ by $y$ by adding the exponents.

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Step 7.1

Move $y$ .

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

Step 7.2

Multiply $y$ by $y^{3}$ .

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Step 7.2.1

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

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

Step 7.2.2

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

$x^{2} y^{1 + 3}$

Step 7.3

Add $1$ and $3$ .

$x^{2} y^{4}$