Verified Answer :

HomertheGenius

Dividing fractions means to invert ( flip over ) the second fraction and multiply:
\(\frac{ \frac{1}{ x^{3} } }{ \frac{3}{ x^{2} } } = \frac{1}{ x^{3} } : \frac{3}{ x^{2} } = \\ \frac{1}{ x^{3} } * \frac{ x^{2} }{3}= \frac{1}{3x}\)
Answer:   1 / 3x

Answer:  Simplified form is \(\frac{1}{3x}\)

Step-by-step explanation:

Since we have given that

\(\frac{\frac{1}{x^3}}{\frac{3}{x^2}}\)

We need to simplify the above expression:

By using "Exponential rule":

\(a^m\div a^n=a^{m-n}\)

\(\frac{\frac{1}{x^3}}{\frac{3}{x^2}}\\\\=\frac{1}{x^3}\times \frac{x^2}{3}\\\\=\frac{1}{3}\times \frac{x^2}{x^3}\\\\=\frac{1}{3x^{3-2}}\\\\=\frac{1}{3x}\)

Hence, Simplified form is \(\frac{1}{3x}\)