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

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

Step 1

Move $v^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

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

Move $v^{2}$ .

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

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

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

Add $2$ and $4$ .

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

Step 3

Cancel the common factor of $u^{3}$ and $u^{2}$ .

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{3 u v^{6}}{4}$