Simplify (3u^4v^2*3u^3v^4)/(u^4v^2)

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

Step 1

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

Move $u^{3}$ .

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

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

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

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.

Move $v^{4}$ .

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

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

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

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 $u^{4}$ .

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

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

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

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

Cancel the common factors.

Multiply by $1$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Step 5

Multiply $3$ by $3$ .

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