Algebra Examples

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

Step 1

Cancel the common factor of $x^{3}$ and $x^{2}$ .

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Step 1.1

Factor $x^{2}$ out of $x^{3} y^{2} z^{3}$ .

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

Step 1.2

Cancel the common factors.

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Step 1.2.1

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

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 2

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

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Step 2.1

Factor $y$ out of $x y^{2} z^{3}$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

Cancel the common factor of $z^{3}$ and $z^{2}$ .

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Step 3.1

Factor $z^{2}$ out of $x y z^{3}$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 3.2.4

Divide $x y z$ by $1$ .

${(x y z)}^{- 2}$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 5

Simplify the denominator.

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Step 5.1

Apply the product rule to $x y z$ .

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

Step 5.2

Apply the product rule to $x y$ .

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