Algebra Examples

$(\frac{1}{2} u^{2} v^{3}) (2 u v^{4})$

Step 1

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

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Step 1.1

Move $u$ .

$\frac{1}{2} \cdot (u \cdot u^{2} v^{3}) (2 v^{4})$

Step 1.2

Multiply $u$ by $u^{2}$ .

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Step 1.2.1

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

$\frac{1}{2} \cdot (u^{1} u^{2} v^{3}) (2 v^{4})$

Step 1.2.2

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

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

Step 1.3

Add $1$ and $2$ .

$\frac{1}{2} \cdot (u^{3} v^{3}) (2 v^{4})$

Step 2

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

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Step 2.1

Move $v^{4}$ .

$\frac{1}{2} \cdot (u^{3} (v^{4} v^{3})) \cdot 2$

Step 2.2

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

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

Step 2.3

Add $4$ and $3$ .

$\frac{1}{2} \cdot (u^{3} v^{7}) \cdot 2$

Step 3

Multiply $\frac{1}{2} (u^{3} v^{7})$ .

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Step 3.1

Combine $u^{3}$ and $\frac{1}{2}$ .

$\frac{u^{3}}{2} v^{7} \cdot 2$

Step 3.2

Combine $\frac{u^{3}}{2}$ and $v^{7}$ .

$\frac{u^{3} v^{7}}{2} \cdot 2$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Cancel the common factor.

$\frac{u^{3} v^{7}}{2} \cdot 2$

Step 4.2

Rewrite the expression.

$u^{3} v^{7}$