Simplify v(uv^2)(u^3v)

$v (u v^{2}) (u^{3} v)$

Step 1

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

Move $v^{2}$ .

$v^{2} v u (u^{3} v)$

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

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

$v^{2} v^{1} u (u^{3} v)$

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

$v^{2 + 1} u (u^{3} v)$

Add $2$ and $1$ .

$v^{3} u (u^{3} v)$

Step 2

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

Move $v$ .

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

Multiply $v$ by $v^{3}$ .

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

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

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

$v^{1 + 3} u \cdot u^{3}$

Add $1$ and $3$ .

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

Step 3

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

Move $u^{3}$ .

$v^{4} (u^{3} u)$

Multiply $u^{3}$ by $u$ .

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

$v^{4} (u^{3} u^{1})$

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

$v^{4} u^{3 + 1}$

Add $3$ and $1$ .

$v^{4} u^{4}$