Algebra Examples

$\frac{8 x^{2} y^{2} z}{x z^{3}} \div \frac{10 x y}{x^{4} z}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{8 x^{2} y^{2} z}{x z^{3}} \cdot \frac{x^{4} z}{10 x y}$

Step 2

Combine.

$\frac{8 x^{2} y^{2} z (x^{4} z)}{x z^{3} (10 x y)}$

Step 3

Multiply $x^{2}$ by $x^{4}$ by adding the exponents.

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Step 3.1

Move $x^{4}$ .

$\frac{8 (x^{4} x^{2}) y^{2} z \cdot z}{x z^{3} (10 x y)}$

Step 3.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{8 x^{4 + 2} y^{2} z \cdot z}{x z^{3} (10 x y)}$

Step 3.3

Add $4$ and $2$ .

$\frac{8 x^{6} y^{2} z \cdot z}{x z^{3} (10 x y)}$

Step 4

Multiply $z$ by $z$ by adding the exponents.

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Step 4.1

Move $z$ .

$\frac{8 x^{6} y^{2} (z \cdot z)}{x z^{3} (10 x y)}$

Step 4.2

Multiply $z$ by $z$ .

$\frac{8 x^{6} y^{2} z^{2}}{x z^{3} (10 x y)}$

Step 5

Multiply $x$ by $x$ by adding the exponents.

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Step 5.1

Move $x$ .

$\frac{8 x^{6} y^{2} z^{2}}{x \cdot x z^{3} (10 y)}$

Step 5.2

Multiply $x$ by $x$ .

$\frac{8 x^{6} y^{2} z^{2}}{x^{2} z^{3} (10 y)}$

Step 6

Cancel the common factor of $8$ and $10$ .

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Step 6.1

Factor $2$ out of $8 x^{6} y^{2} z^{2}$ .

$\frac{2 (4 x^{6} y^{2} z^{2})}{x^{2} z^{3} (10 y)}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $x^{2} z^{3} (10 y)$ .

$\frac{2 (4 x^{6} y^{2} z^{2})}{2 (x^{2} z^{3} (5 y))}$

Step 6.2.2

Cancel the common factor.

$\frac{2 (4 x^{6} y^{2} z^{2})}{2 (x^{2} z^{3} (5 y))}$

Step 6.2.3

Rewrite the expression.

$\frac{4 x^{6} y^{2} z^{2}}{x^{2} z^{3} (5 y)}$

Step 7

Cancel the common factor of $x^{6}$ and $x^{2}$ .

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Step 7.1

Factor $x^{2}$ out of $4 x^{6} y^{2} z^{2}$ .

$\frac{x^{2} (4 x^{4} y^{2} z^{2})}{x^{2} z^{3} (5 y)}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $x^{2}$ out of $x^{2} z^{3} (5 y)$ .

$\frac{x^{2} (4 x^{4} y^{2} z^{2})}{x^{2} (z^{3} (5 y))}$

Step 7.2.2

Cancel the common factor.

$\frac{x^{2} (4 x^{4} y^{2} z^{2})}{x^{2} (z^{3} (5 y))}$

Step 7.2.3

Rewrite the expression.

$\frac{4 x^{4} y^{2} z^{2}}{z^{3} (5 y)}$

Step 8

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

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Step 8.1

Factor $y$ out of $4 x^{4} y^{2} z^{2}$ .

$\frac{y (4 x^{4} y z^{2})}{z^{3} (5 y)}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $y$ out of $z^{3} (5 y)$ .

$\frac{y (4 x^{4} y z^{2})}{y (z^{3} \cdot (5))}$

Step 8.2.2

Cancel the common factor.

$\frac{y (4 x^{4} y z^{2})}{y (z^{3} \cdot (5))}$

Step 8.2.3

Rewrite the expression.

$\frac{4 x^{4} y z^{2}}{z^{3} \cdot (5)}$

Step 9

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

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Step 9.1

Factor $z^{2}$ out of $4 x^{4} y z^{2}$ .

$\frac{z^{2} (4 x^{4} y)}{z^{3} \cdot (5)}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $z^{2}$ out of $z^{3} \cdot (5)$ .

$\frac{z^{2} (4 x^{4} y)}{z^{2} (z \cdot 5)}$

Step 9.2.2

Cancel the common factor.

$\frac{z^{2} (4 x^{4} y)}{z^{2} (z \cdot 5)}$

Step 9.2.3

Rewrite the expression.

$\frac{4 x^{4} y}{z \cdot 5}$

Step 10

Move $5$ to the left of $z$ .

$\frac{4 x^{4} y}{5 z}$