Simplify (1/2u^2v^3)(2uv^4)

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

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

Move $u$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

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

Move $v^{4}$ .

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

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

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

Add $4$ and $3$ .

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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