Algebra Examples

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

Step 1

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

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Step 1.1

Factor $x$ out of ${(- 2)}^{3} x^{4} {(y z)}^{2}$ .

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

Step 1.2

Cancel the common factors.

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Step 1.2.1

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

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $y z$ .

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

Step 2.2

Raise $- 2$ to the power of $3$ .

$\frac{- 8 x^{3} y^{2} z^{2}}{3^{2} y^{3} z}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Raise $3$ to the power of $2$ .

$\frac{- 8 x^{3} y^{2} z^{2}}{9 y^{3} z}$

Step 3.2

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

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Step 3.2.1

Factor $y^{2}$ out of $- 8 x^{3} y^{2} z^{2}$ .

$\frac{y^{2} (- 8 x^{3} z^{2})}{9 y^{3} z}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $y^{2}$ out of $9 y^{3} z$ .

$\frac{y^{2} (- 8 x^{3} z^{2})}{y^{2} (9 y z)}$

Step 3.2.2.2

Cancel the common factor.

$\frac{y^{2} (- 8 x^{3} z^{2})}{y^{2} (9 y z)}$

Step 3.2.2.3

Rewrite the expression.

$\frac{- 8 x^{3} z^{2}}{9 y z}$

Step 3.3

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

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Step 3.3.1

Factor $z$ out of $- 8 x^{3} z^{2}$ .

$\frac{z (- 8 x^{3} z)}{9 y z}$

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Factor $z$ out of $9 y z$ .

$\frac{z (- 8 x^{3} z)}{z (9 y)}$

Step 3.3.2.2

Cancel the common factor.

$\frac{z (- 8 x^{3} z)}{z (9 y)}$

Step 3.3.2.3

Rewrite the expression.

$\frac{- 8 x^{3} z}{9 y}$

Step 3.4

Move the negative in front of the fraction.

$- \frac{8 x^{3} z}{9 y}$