Divide. State the quotient in simplest form, and express the domain of the expression. \( \frac{4}{3 x^{5}} \div \frac{12}{5 x^{7}} \) \( \begin{array}{l}\frac{9}{5 x^{2}}, x \neq 0 \\ \frac{5 x^{2}}{9}, x \neq 0 \\ \frac{16}{5 x^{12}}, x \neq 0 \\ \frac{15 x^{12}}{48}, x \neq 0\end{array} \)

To divide the two fractions, we can multiply by the reciprocal of the second fraction: \[ \frac{4}{3 x^{5}} \div \frac{12}{5 x^{7}} = \frac{4}{3 x^{5}} \times \frac{5 x^{7}}{12} \] Multiply the numerators and the denominators: \[ = \frac{4 \cdot 5 x^{7}}{3 x^{5} \cdot 12} = \frac{20 x^{7}}{36 x^{5}} \] Now divide \( x^{7} \) by \( x^{5} \) (subtract exponents): \[ = \frac{20}{36} x^{2} = \frac{5}{9} x^{2} \] So, the simplest form is: \(\frac{5}{9} x^{2}\) The domain is all real numbers except \( x \neq 0 \) due to the division by zero in the original expression. For the answer choices, the right summary would be \(\frac{5}{9} x^{2}, x \neq 0\).