Algebra Examples

${(\frac{x^{2} y^{6}}{x^{- 1} y^{3}})}^{\frac{1}{3}}$

Step 1

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

${(\frac{x^{2} y^{6} x}{y^{3}})}^{\frac{1}{3}}$

Step 2

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 2.1

Move $x$ .

${(\frac{x \cdot x^{2} y^{6}}{y^{3}})}^{\frac{1}{3}}$

Step 2.2

Multiply $x$ by $x^{2}$ .

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Step 2.2.1

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

${(\frac{x^{1} x^{2} y^{6}}{y^{3}})}^{\frac{1}{3}}$

Step 2.2.2

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

${(\frac{x^{1 + 2} y^{6}}{y^{3}})}^{\frac{1}{3}}$

Step 2.3

Add $1$ and $2$ .

${(\frac{x^{3} y^{6}}{y^{3}})}^{\frac{1}{3}}$

Step 3

Cancel the common factor of $y^{6}$ and $y^{3}$ .

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Step 3.1

Factor $y^{3}$ out of $x^{3} y^{6}$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 3.2.4

Divide $x^{3} y^{3}$ by $1$ .

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

Step 4

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

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

Step 5

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

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Step 5.1

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

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

Step 5.2

Cancel the common factor of $3$ .

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Step 5.2.1

Cancel the common factor.

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

Step 5.2.2

Rewrite the expression.

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

Step 6

Simplify.

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

Step 7

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

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Step 7.1

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

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

Step 7.2

Cancel the common factor of $3$ .

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Step 7.2.1

Cancel the common factor.

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

Step 7.2.2

Rewrite the expression.

$x y^{1}$

Step 8

Simplify.

$x y$