Simplify ((7c^-3d^3)/(c^5dh^-4))^-1

${(\frac{7 c^{- 3} d^{3}}{c^{5} d h^{- 4}})}^{- 1}$

Step 1

Move $c^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{7 d^{3}}{c^{5} d h^{- 4} c^{3}})}^{- 1}$

Step 2

Multiply $c^{5}$ by $c^{3}$ by adding the exponents.

Move $c^{3}$ .

${(\frac{7 d^{3}}{c^{3} c^{5} d h^{- 4}})}^{- 1}$

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

${(\frac{7 d^{3}}{c^{3 + 5} d h^{- 4}})}^{- 1}$

Add $3$ and $5$ .

${(\frac{7 d^{3}}{c^{8} d h^{- 4}})}^{- 1}$

Step 3

Move $h^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{7 d^{3} h^{4}}{c^{8} d})}^{- 1}$

Step 4

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

Factor $d$ out of $7 d^{3} h^{4}$ .

${(\frac{d (7 d^{2} h^{4})}{c^{8} d})}^{- 1}$

Cancel the common factors.

Factor $d$ out of $c^{8} d$ .

${(\frac{d (7 d^{2} h^{4})}{d c^{8}})}^{- 1}$

Cancel the common factor.

${(\frac{d (7 d^{2} h^{4})}{d c^{8}})}^{- 1}$

Rewrite the expression.

${(\frac{7 d^{2} h^{4}}{c^{8}})}^{- 1}$

Step 5

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

$\frac{c^{8}}{7 d^{2} h^{4}}$