Algebra Examples

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

Step 1

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

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Step 1.1

Factor $x$ out of $2 x y^{2}$ .

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

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $x$ out of $x^{4} y$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 2

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

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Step 2.1

Factor $y$ out of $2 y^{2}$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

Change the sign of the exponent by rewriting the base as its reciprocal.

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

Step 4

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 4.1

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

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

Step 4.2

Apply the product rule to $2 y$ .

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

Step 5

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

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Step 5.1

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

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

Step 5.2

Multiply $3$ by $2$ .

$\frac{x^{6}}{2^{2} y^{2}}$

Step 6

Raise $2$ to the power of $2$ .

$\frac{x^{6}}{4 y^{2}}$