Question

simplifying rational expressions\which shows the following expression after the negative exponents have been eliminated?\\$\frac{m^7n^3}{mn^{-1}}, m\
eq0, n\
eq0$\options: $\frac{mn}{m^7n}$, $\frac{m^7n^3n}{m}$, $m^7n^3mn$, $\frac{m^7n^3}{m(-n)}$

Explanation:

Step1: Rewrite negative exponent

Recall that $a^{-1}=\frac{1}{a}$, so $mn^{-1}=\frac{m}{n}$. Substitute this into the original expression:
$\frac{m^7n^3}{\frac{m}{n}}$

Step2: Divide by fraction (multiply by reciprocal)

Dividing by a fraction is equivalent to multiplying by its reciprocal:
$m^7n^3 \times \frac{n}{m}$

Step3: Rewrite as single fraction

Combine the terms into one fraction:
$\frac{m^7n^3 \times n}{m}$

Step4: Simplify the expression

Cancel one $m$ from numerator and denominator, and combine $n$ terms using $n^a \times n^b = n^{a+b}$:
$\frac{m^6n^4}{1}$ is not needed; instead, match to options by rearranging the multiplication step result to $\frac{m^7n^3n}{m} = \frac{m^7n^4}{m}$, which is equivalent to $\frac{m^7n^3n}{m}$ (matches the structure of the second option).

Answer:

$\boldsymbol{\frac{m^7n^3n}{m}}$ (the second option)