Algebra Examples

$(\frac{4 x y^{- 4} z^{3}}{12 x^{2} y z^{- 2}}) \cdot 2$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{4 x \frac{1}{y^{4}} z^{3}}{12 x^{2} y z^{- 2}} \cdot 2$

Step 1.2

Combine exponents.

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Step 1.2.1

Combine $4$ and $\frac{1}{y^{4}}$ .

$\frac{x \frac{4}{y^{4}} z^{3}}{12 x^{2} y z^{- 2}} \cdot 2$

Step 1.2.2

Combine $x$ and $\frac{4}{y^{4}}$ .

$\frac{\frac{x \cdot 4}{y^{4}} z^{3}}{12 x^{2} y z^{- 2}} \cdot 2$

Step 1.2.3

Combine $\frac{x \cdot 4}{y^{4}}$ and $z^{3}$ .

$\frac{\frac{x \cdot 4 z^{3}}{y^{4}}}{12 x^{2} y z^{- 2}} \cdot 2$

Step 1.3

Move $4$ to the left of $x$ .

$\frac{\frac{4 x z^{3}}{y^{4}}}{12 x^{2} y z^{- 2}} \cdot 2$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{\frac{4 x z^{3}}{y^{4}}}{12 x^{2} y \frac{1}{z^{2}}} \cdot 2$

Step 2.2

Combine exponents.

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Step 2.2.1

Combine $12$ and $\frac{1}{z^{2}}$ .

$\frac{\frac{4 x z^{3}}{y^{4}}}{x^{2} y \frac{12}{z^{2}}} \cdot 2$

Step 2.2.2

Combine $x^{2}$ and $\frac{12}{z^{2}}$ .

$\frac{\frac{4 x z^{3}}{y^{4}}}{y \frac{x^{2} \cdot 12}{z^{2}}} \cdot 2$

Step 2.2.3

Combine $y$ and $\frac{x^{2} \cdot 12}{z^{2}}$ .

$\frac{\frac{4 x z^{3}}{y^{4}}}{\frac{y (x^{2} \cdot 12)}{z^{2}}} \cdot 2$

Step 2.3

Remove unnecessary parentheses.

$\frac{\frac{4 x z^{3}}{y^{4}}}{\frac{y x^{2} \cdot 12}{z^{2}}} \cdot 2$

Step 2.4

Move $12$ to the left of $y x^{2}$ .

$\frac{\frac{4 x z^{3}}{y^{4}}}{\frac{12 y x^{2}}{z^{2}}} \cdot 2$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{4 x z^{3}}{y^{4}} \cdot \frac{z^{2}}{12 y x^{2}} \cdot 2$

Step 4

Combine.

$\frac{4 x z^{3} z^{2}}{y^{4} (12 y x^{2})} \cdot 2$

Step 5

Multiply $z^{3}$ by $z^{2}$ by adding the exponents.

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Step 5.1

Move $z^{2}$ .

$\frac{4 x (z^{2} z^{3})}{y^{4} (12 y x^{2})} \cdot 2$

Step 5.2

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

$\frac{4 x z^{2 + 3}}{y^{4} (12 y x^{2})} \cdot 2$

Step 5.3

Add $2$ and $3$ .

$\frac{4 x z^{5}}{y^{4} (12 y x^{2})} \cdot 2$

Step 6

Multiply $y^{4}$ by $y$ by adding the exponents.

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Step 6.1

Move $y$ .

$\frac{4 x z^{5}}{y \cdot y^{4} (12 x^{2})} \cdot 2$

Step 6.2

Multiply $y$ by $y^{4}$ .

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Step 6.2.1

Raise $y$ to the power of $1$ .

$\frac{4 x z^{5}}{y^{1} y^{4} (12 x^{2})} \cdot 2$

Step 6.2.2

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

$\frac{4 x z^{5}}{y^{1 + 4} (12 x^{2})} \cdot 2$

Step 6.3

Add $1$ and $4$ .

$\frac{4 x z^{5}}{y^{5} (12 x^{2})} \cdot 2$

Step 7

Cancel the common factor of $2$ .

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Step 7.1

Factor $2$ out of $y^{5} \cdot 12 x^{2}$ .

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

Step 7.2

Cancel the common factor.

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

Step 7.3

Rewrite the expression.

$\frac{4 x z^{5}}{y^{5} \cdot 6 x^{2}}$

Step 8

Cancel the common factor of $4$ and $6$ .

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Step 8.1

Factor $2$ out of $4 x z^{5}$ .

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

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $2$ out of $y^{5} \cdot 6 x^{2}$ .

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

Step 8.2.2

Cancel the common factor.

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

Step 8.2.3

Rewrite the expression.

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

Step 9

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

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Step 9.1

Factor $x$ out of $2 x z^{5}$ .

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

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $x$ out of $y^{5} \cdot 3 x^{2}$ .

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

Step 9.2.2

Cancel the common factor.

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

Step 9.2.3

Rewrite the expression.

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

Step 10

Move $3$ to the left of $y^{5}$ .

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