Simplify ((p^3q^4r^2)/(p^2qr^4))^-1

${(\frac{p^{3} q^{4} r^{2}}{p^{2} q r^{4}})}^{- 1}$

Step 1

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

Factor $p^{2}$ out of $p^{3} q^{4} r^{2}$ .

${(\frac{p^{2} (p q^{4} r^{2})}{p^{2} q r^{4}})}^{- 1}$

Cancel the common factors.

Factor $p^{2}$ out of $p^{2} q r^{4}$ .

${(\frac{p^{2} (p q^{4} r^{2})}{p^{2} (q r^{4})})}^{- 1}$

Cancel the common factor.

${(\frac{p^{2} (p q^{4} r^{2})}{p^{2} (q r^{4})})}^{- 1}$

Rewrite the expression.

${(\frac{p q^{4} r^{2}}{q r^{4}})}^{- 1}$

Step 2

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

Factor $q$ out of $p q^{4} r^{2}$ .

${(\frac{q (p q^{3} r^{2})}{q r^{4}})}^{- 1}$

Cancel the common factors.

Factor $q$ out of $q r^{4}$ .

${(\frac{q (p q^{3} r^{2})}{q (r^{4})})}^{- 1}$

Cancel the common factor.

${(\frac{q (p q^{3} r^{2})}{q r^{4}})}^{- 1}$

Rewrite the expression.

${(\frac{p q^{3} r^{2}}{r^{4}})}^{- 1}$

Step 3

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

Factor $r^{2}$ out of $p q^{3} r^{2}$ .

${(\frac{r^{2} (p q^{3})}{r^{4}})}^{- 1}$

Cancel the common factors.

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

${(\frac{r^{2} (p q^{3})}{r^{2} r^{2}})}^{- 1}$

Cancel the common factor.

${(\frac{r^{2} (p q^{3})}{r^{2} r^{2}})}^{- 1}$

Rewrite the expression.

${(\frac{p q^{3}}{r^{2}})}^{- 1}$

Step 4

Change the sign of the exponent by rewriting the base as its reciprocal.

$\frac{r^{2}}{p q^{3}}$