which shows the following expression after the negative exponents have been eliminated?\n$\frac{m^{7}n^{3}}{m…

Explanation:

Step1: Apply negative - exponent rule

Recall that $a^{-b}=\frac{1}{a^{b}}$. So, $n^{-1}=\frac{1}{n}$, and $\frac{m^{7}n^{3}}{mn^{-1}}=\frac{m^{7}n^{3}}{\frac{m}{n}}$.

Step2: Simplify the complex - fraction

When dividing by a fraction, we multiply by its reciprocal. So, $\frac{m^{7}n^{3}}{\frac{m}{n}}=m^{7}n^{3}\times\frac{n}{m}$.

Step3: Use the rules of exponents for multiplication and division

For multiplication of terms with the same base $a^{m}\times a^{n}=a^{m + n}$, and for division $a^{m}\div a^{n}=a^{m - n}$. So, $m^{7}n^{3}\times\frac{n}{m}=\frac{m^{7}n^{3}n}{m}=\frac{m^{7}n^{4}}{m}=m^{7 - 1}n^{4}=m^{6}n^{4}$. Also, $\frac{m^{7}n^{3}n}{m}$ is equivalent to the first option after simplification.

Answer:

A. $\frac{m^{7}n^{3}n}{m}$