Simplify ((14w^12)/(7w^3))^-1

${(\frac{14 w^{12}}{7 w^{3}})}^{- 1}$

Cancel the common factor of $14$ and $7$ .

Factor $7$ out of $14 w^{12}$ .

${(\frac{7 (2 w^{12})}{7 w^{3}})}^{- 1}$

Cancel the common factors.

Factor $7$ out of $7 w^{3}$ .

${(\frac{7 (2 w^{12})}{7 (w^{3})})}^{- 1}$

Cancel the common factor.

${(\frac{7 (2 w^{12})}{7 w^{3}})}^{- 1}$

Rewrite the expression.

${(\frac{2 w^{12}}{w^{3}})}^{- 1}$

Cancel the common factor of $w^{12}$ and $w^{3}$ .

Factor $w^{3}$ out of $2 w^{12}$ .

${(\frac{w^{3} (2 w^{9})}{w^{3}})}^{- 1}$

Cancel the common factors.

Multiply by $1$ .

${(\frac{w^{3} (2 w^{9})}{w^{3} \cdot 1})}^{- 1}$

Cancel the common factor.

${(\frac{w^{3} (2 w^{9})}{w^{3} \cdot 1})}^{- 1}$

Rewrite the expression.

${(\frac{2 w^{9}}{1})}^{- 1}$

Divide $2 w^{9}$ by $1$ .

${(2 w^{9})}^{- 1}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{2 w^{9}}$