Algebra Examples

$(2 u^{4} v^{3}) \cdot (- 3 c^{5} d^{4}) \cdot (\frac{1}{2} c^{3} u^{2} v^{4})$

Step 1

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

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Step 1.1

Move $u^{2}$ .

$2 (u^{2} u^{4}) v^{3} \cdot (- 3 c^{5} d^{4}) \cdot (\frac{1}{2} \cdot (c^{3} v^{4}))$

Step 1.2

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

$2 u^{2 + 4} v^{3} \cdot (- 3 c^{5} d^{4}) \cdot (\frac{1}{2} \cdot (c^{3} v^{4}))$

Step 1.3

Add $2$ and $4$ .

$2 u^{6} v^{3} \cdot (- 3 c^{5} d^{4}) \cdot (\frac{1}{2} \cdot (c^{3} v^{4}))$

Step 2

Multiply $v^{3}$ by $v^{4}$ by adding the exponents.

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Step 2.1

Move $v^{4}$ .

$2 u^{6} (v^{4} v^{3}) \cdot (- 3 c^{5} d^{4}) \cdot (\frac{1}{2} \cdot (c^{3}))$

Step 2.2

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

$2 u^{6} v^{4 + 3} \cdot (- 3 c^{5} d^{4}) \cdot (\frac{1}{2} \cdot (c^{3}))$

Step 2.3

Add $4$ and $3$ .

$2 u^{6} v^{7} \cdot (- 3 c^{5} d^{4}) \cdot (\frac{1}{2} \cdot (c^{3}))$

Step 3

Multiply $c^{5}$ by $c^{3}$ by adding the exponents.

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Step 3.1

Move $c^{3}$ .

$2 u^{6} v^{7} \cdot (- 3 (c^{3} c^{5}) d^{4}) \cdot \frac{1}{2}$

Step 3.2

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

$2 u^{6} v^{7} \cdot (- 3 c^{3 + 5} d^{4}) \cdot \frac{1}{2}$

Step 3.3

Add $3$ and $5$ .

$2 u^{6} v^{7} \cdot (- 3 c^{8} d^{4}) \cdot \frac{1}{2}$

Step 4

Multiply $- 3$ by $2$ .

$- 6 u^{6} v^{7} (c^{8} d^{4}) \cdot \frac{1}{2}$

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Factor $2$ out of $- 6 u^{6} v^{7} (c^{8} d^{4})$ .

$2 (- 3 u^{6} v^{7} (c^{8} d^{4})) \cdot \frac{1}{2}$

Step 5.2

Cancel the common factor.

$2 (- 3 u^{6} v^{7} (c^{8} d^{4})) \cdot \frac{1}{2}$

Step 5.3

Rewrite the expression.

$- 3 u^{6} v^{7} (c^{8} d^{4})$

$- 3 u^{6} v^{7} c^{8} d^{4}$