Let's simplify the given expression step by step:
Given expression:
[tex]\[
\frac{m^7 n^3}{m n^{-1}}
\][/tex]
### Step 1: Eliminate the negative exponent [tex]\( n^{-1} \)[/tex]
Recall that [tex]\( n^{-1} \)[/tex] is the same as [tex]\( \frac{1}{n} \)[/tex]. Therefore, we can rewrite the denominator:
[tex]\[
\frac{m^7 n^3}{m \cdot \frac{1}{n}} = \frac{m^7 n^3}{\frac{m}{n}}
\][/tex]
### Step 2: Simplify the fraction
When dividing by a fraction, it's equivalent to multiplying by its reciprocal:
[tex]\[
\frac{m^7 n^3}{\frac{m}{n}} = m^7 n^3 \cdot \frac{n}{m}
\][/tex]
### Step 3: Combine and simplify the exponents
Now we combine the terms:
[tex]\[
m^7 n^3 \cdot \frac{n}{m} = m^{7-1} \cdot n^{3+1} = m^6 \cdot n^4
\][/tex]
Thus, the expression simplifies to:
[tex]\[
m^6 n^4
\][/tex]
### Final Answer:
The result shows that after eliminating negative exponents, the given expression simplifies to:
[tex]\[
m^6 n^4
\][/tex]
