Simplify. Write your answer as a proper or improper fraction in simplest form. (frac (50)/(33))((13)/(32))=(square )/(square )

To simplify the given expression, we need to divide the fraction $\frac{50}{33}$ by the fraction $\frac{13}{32}$.<br /><br />To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping the numerator and denominator.<br /><br />So, the reciprocal of $\frac{13}{32}$ is $\frac{32}{13}$.<br /><br />Now, we can rewrite the given expression as:<br /><br />$\frac{\frac{50}{33}}{\frac{13}{32}} = \frac{50}{33} \times \frac{32}{13}$<br /><br />To multiply fractions, we multiply the numerators together and the denominators together.<br /><br />Multiplying the numerators: $50 \times 32 = 1600$<br /><br />Multiplying the denominators: $33 \times 13 = 429$<br /><br />Therefore, the simplified expression is:<br /><br />$\frac{1600}{429}$<br /><br />This fraction is already in its simplest form, as the numerator and denominator have no common factors other than 1.<br /><br />So, the final answer is:<br /><br />$\frac{1600}{429}$