Question

Reduce this algebraic fraction 27c^4d^5/9c^7d^4 ...?

Answer 1

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 $\frac{ x^{a} }{ x^{b}} = x^{a-b} = \frac{1}{ x^{b-a} }$:
$\frac{27}{9}*\frac{c^{4}}{c^{7}}*\frac{d^{5}}{d^{4} }=3* \frac{1}{c^{7-4}} * d^{5-4} =3* \frac{1}{ c^{3} } *d^{1}= \frac{3d}{ c^{3} }$