Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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Step 1.1.1

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

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

Step 1.1.2

Cancel the common factor of $2$ .

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Step 1.1.2.1

Factor $2$ out of $4$ .

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

Step 1.1.2.2

Cancel the common factor.

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

Step 1.1.2.3

Rewrite the expression.

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

Step 1.2

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

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

Step 1.3

Multiply the exponents in ${(x^{2})}^{2}$ .

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Step 1.3.1

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

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

Step 1.3.2

Multiply $2$ by $2$ .

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

Step 2

Simplify the denominator.

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Step 2.1

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

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Step 2.1.1

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

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

Step 2.1.2

Cancel the common factor of $2$ .

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Step 2.1.2.1

Factor $2$ out of $4$ .

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

Step 2.1.2.2

Cancel the common factor.

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

Step 2.1.2.3

Rewrite the expression.

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

Step 2.2

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

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

Step 2.3

Multiply the exponents in ${(x^{2})}^{2}$ .

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Step 2.3.1

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

$\frac{x^{4} y^{2}}{x^{2 \cdot 2} y^{2}}$

Step 2.3.2

Multiply $2$ by $2$ .

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

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $x^{4}$ .

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Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

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

Step 3.2

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

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Rewrite the expression.

$1$