Algebra Examples

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

Step 1

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

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Step 1.1

Move $u^{3}$ .

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

Step 1.2

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

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

Step 1.3

Add $3$ and $4$ .

$\frac{3 u^{7} v^{2} \cdot (3 v^{4})}{u^{4} v^{2}}$

Step 2

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

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Step 2.1

Move $v^{4}$ .

$\frac{3 u^{7} (v^{4} v^{2}) \cdot 3}{u^{4} v^{2}}$

Step 2.2

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

$\frac{3 u^{7} v^{4 + 2} \cdot 3}{u^{4} v^{2}}$

Step 2.3

Add $4$ and $2$ .

$\frac{3 u^{7} v^{6} \cdot 3}{u^{4} v^{2}}$

Step 3

Cancel the common factor of $u^{7}$ and $u^{4}$ .

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Step 3.1

Factor $u^{4}$ out of $3 u^{7} v^{6} \cdot 3$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $u^{4}$ out of $u^{4} v^{2}$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

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

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Step 4.1

Factor $v^{2}$ out of $3 u^{3} v^{6} \cdot 3$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Multiply by $1$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 4.2.4

Divide $3 u^{3} v^{4} \cdot 3$ by $1$ .

$3 u^{3} v^{4} \cdot 3$

Step 5

Multiply $3$ by $3$ .

$9 u^{3} v^{4}$