https://r2.erweima.ai/mathbot/image/17235784537744cawxp7t.jpg

To solve the division of the monomials given in the image:

\[
\frac{45m^7n}{15mn}
\]

We can follow these steps:

1. **Divide the coefficients**: 
   \[
   \frac{45}{15} = 3
   \]

2. **Apply the quotient rule for exponents**:
   - For the variable \(m\):
     \[
     \frac{m^7}{m} = m^{7-1} = m^6
     \]
   - For the variable \(n\):
     \[
     \frac{n}{n} = n^{1-1} = n^0 = 1
     \]

So the expression simplifies to:

\[
3m^6
\]

Thus, the solution is:

\[
\frac{45m^7n}{15mn} = 3m^6
\]

Would you like more details or have any further questions?

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**Related questions:**

1. What happens when dividing monomials with the same base but different exponents?
2. How do you handle division when the exponent in the denominator is larger than in the numerator?
3. What if the exponents were negative in this scenario?
4. Can you explain the quotient rule for exponents in more detail?
5. How does division affect coefficients in a monomial?
6. What is the outcome if the numerator has no common variables with the denominator?
7. How would the expression change if there was an additional variable in the denominator?
8. What is the result if \( n \) was raised to a higher power in the numerator?

**Tip:** Always simplify coefficients first before applying exponent rules to variables. This reduces the complexity of the expression right from the beginning.

Aprende a resolver la división de monomios con este ejemplo detallado. Incluye el uso de reglas de exponentes y simplificación de coeficientes. Ideal para estudiantes de los grados 7-9.

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