The answer is \(\frac{3d}{ c^{3}}\)
The fraction is: \(\frac{27 c^{4} d^{5}}{9 c^{7} d^{4} }\)
Let's rewrite it: \(\frac{27 c^{4} d^{5}}{9 c^{7} d^{4} }= \frac{27}{9}*\frac{c^{4}}{c^{7}}*\frac{d^{5}}{d^{4} }\)
Now, let's use the rule \(\frac{ x^{a} }{ x^{b}} = x^{a-b} = \frac{1}{ x^{b-a} }\):
\(\frac{27}{9}*\frac{c^{4}}{c^{7}}*\frac{d^{5}}{d^{4} }=3* \frac{1}{c^{7-4}} * d^{5-4} =3* \frac{1}{ c^{3} } *d^{1}= \frac{3d}{ c^{3} }\)
