Algebra Examples

$\frac{{(x^{6} y^{3})}^{- \frac{1}{3}}}{{(x^{4} y^{2})}^{- \frac{1}{2}}}$

Step 1

Simplify the expression.

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Step 1.1

Move ${(x^{6} y^{3})}^{- \frac{1}{3}}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(x^{4} y^{2})}^{- \frac{1}{2}} {(x^{6} y^{3})}^{\frac{1}{3}}}$

Step 1.2

Move ${(x^{4} y^{2})}^{- \frac{1}{2}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(x^{4} y^{2})}^{\frac{1}{2}}}{{(x^{6} y^{3})}^{\frac{1}{3}}}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $x^{4} y^{2}$ .

$\frac{{(x^{4})}^{\frac{1}{2}} {(y^{2})}^{\frac{1}{2}}}{{(x^{6} y^{3})}^{\frac{1}{3}}}$

Step 2.2

Multiply the exponents in ${(x^{4})}^{\frac{1}{2}}$ .

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Step 2.2.1

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

$\frac{x^{4 (\frac{1}{2})} {(y^{2})}^{\frac{1}{2}}}{{(x^{6} y^{3})}^{\frac{1}{3}}}$

Step 2.2.2

Cancel the common factor of $2$ .

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Step 2.2.2.1

Factor $2$ out of $4$ .

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

Step 2.2.2.2

Cancel the common factor.

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

Step 2.2.2.3

Rewrite the expression.

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

Step 2.3

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

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Step 2.3.1

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

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

Step 2.3.2

Cancel the common factor of $2$ .

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Step 2.3.2.1

Cancel the common factor.

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

Step 2.3.2.2

Rewrite the expression.

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

Step 2.4

Simplify.

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

Step 3

Simplify the denominator.

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Step 3.1

Apply the product rule to $x^{6} y^{3}$ .

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

Step 3.2

Multiply the exponents in ${(x^{6})}^{\frac{1}{3}}$ .

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Step 3.2.1

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

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

Step 3.2.2

Cancel the common factor of $3$ .

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Step 3.2.2.1

Factor $3$ out of $6$ .

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

Step 3.2.2.2

Cancel the common factor.

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

Step 3.2.2.3

Rewrite the expression.

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

Step 3.3

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

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Step 3.3.1

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

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

Step 3.3.2

Cancel the common factor of $3$ .

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Step 3.3.2.1

Cancel the common factor.

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

Step 3.3.2.2

Rewrite the expression.

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

Step 3.4

Simplify.

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

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of $x^{2}$ .

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Step 4.1.1

Cancel the common factor.

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

Step 4.1.2

Rewrite the expression.

$\frac{y}{y}$

Step 4.2

Cancel the common factor of $y$ .

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Step 4.2.1

Cancel the common factor.

$\frac{y}{y}$

Step 4.2.2

Rewrite the expression.

$1$