Algebra Examples

$(\frac{5 v^{3}}{u^{6}}) (- \frac{6 u^{2}}{v^{4}})$

Step 1

Rewrite using the commutative property of multiplication.

$- \frac{5 v^{3}}{u^{6}} \cdot \frac{6 u^{2}}{v^{4}}$

Step 2

Cancel the common factor of $v^{3}$ .

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Step 2.1

Move the leading negative in $- \frac{5 v^{3}}{u^{6}}$ into the numerator.

$\frac{- 5 v^{3}}{u^{6}} \cdot \frac{6 u^{2}}{v^{4}}$

Step 2.2

Factor $v^{3}$ out of $- 5 v^{3}$ .

$\frac{v^{3} \cdot - 5}{u^{6}} \cdot \frac{6 u^{2}}{v^{4}}$

Step 2.3

Factor $v^{3}$ out of $v^{4}$ .

$\frac{v^{3} \cdot - 5}{u^{6}} \cdot \frac{6 u^{2}}{v^{3} v}$

Step 2.4

Cancel the common factor.

$\frac{v^{3} \cdot - 5}{u^{6}} \cdot \frac{6 u^{2}}{v^{3} v}$

Step 2.5

Rewrite the expression.

$\frac{- 5}{u^{6}} \cdot \frac{6 u^{2}}{v}$

Step 3

Cancel the common factor of $u^{2}$ .

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Step 3.1

Factor $u^{2}$ out of $u^{6}$ .

$\frac{- 5}{u^{2} u^{4}} \cdot \frac{6 u^{2}}{v}$

Step 3.2

Factor $u^{2}$ out of $6 u^{2}$ .

$\frac{- 5}{u^{2} u^{4}} \cdot \frac{u^{2} \cdot 6}{v}$

Step 3.3

Cancel the common factor.

$\frac{- 5}{u^{2} u^{4}} \cdot \frac{u^{2} \cdot 6}{v}$

Step 3.4

Rewrite the expression.

$\frac{- 5}{u^{4}} \cdot \frac{6}{v}$

Step 4

Multiply $\frac{- 5}{u^{4}}$ by $\frac{6}{v}$ .

$\frac{- 5 \cdot 6}{u^{4} v}$

Step 5

Simplify the expression.

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Step 5.1

Multiply $- 5$ by $6$ .

$\frac{- 30}{u^{4} v}$

Step 5.2

Move the negative in front of the fraction.

$- \frac{30}{u^{4} v}$