Simplify (-20(m^2v)(-v)^3)/(5(-v)^2(-m^4))

$\frac{- 20 (m^{2} v) {(- v)}^{3}}{5 {(- v)}^{2} (- m^{4})}$

Step 1

Cancel the common factor of $- 20$ and $5$ .

Factor $5$ out of $- 20 (m^{2} v) {(- v)}^{3}$ .

$\frac{5 (- 4 (m^{2} v) {(- v)}^{3})}{5 {(- v)}^{2} (- m^{4})}$

Cancel the common factors.

Factor $5$ out of $5 {(- v)}^{2} (- m^{4})$ .

$\frac{5 (- 4 (m^{2} v) {(- v)}^{3})}{5 ({(- v)}^{2} (- m^{4}))}$

Cancel the common factor.

$\frac{5 (- 4 (m^{2} v) {(- v)}^{3})}{5 ({(- v)}^{2} (- m^{4}))}$

Rewrite the expression.

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

Step 2

Cancel the common factor of $m^{2}$ and $m^{4}$ .

Factor $m^{2}$ out of $- 4 (m^{2} v) {(- v)}^{3}$ .

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

Cancel the common factors.

Factor $m^{2}$ out of ${(- v)}^{2} (- m^{4})$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Cancel the common factor of ${(- v)}^{3}$ and ${(- v)}^{2}$ .

Factor ${(- v)}^{2}$ out of $- 4 (v) {(- v)}^{3}$ .

$\frac{{(- v)}^{2} (- 4 (v) (- v))}{{(- v)}^{2} (- m^{2})}$

Cancel the common factors.

Cancel the common factor.

$\frac{{(- v)}^{2} (- 4 (v) (- v))}{{(- v)}^{2} (- m^{2})}$

Rewrite the expression.

$\frac{- 4 (v) (- v)}{- m^{2}}$

Step 4

Dividing two negative values results in a positive value.

$\frac{- 4 (v) (v)}{m^{2}}$

Step 5

Multiply $v$ by $v$ by adding the exponents.

Move $v$ .

$\frac{- 4 (v \cdot v)}{m^{2}}$

Multiply $v$ by $v$ .

$\frac{- 4 v^{2}}{m^{2}}$

Step 6

Move the negative in front of the fraction.

$- \frac{4 v^{2}}{m^{2}}$