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The problem asks to divide the monomial \( 16x^5y^7 \) by the monomial \( 4x^2y^3 \). Let's work through the solution.

### Step-by-step division:

1. **Divide the coefficients**:
   \[
   \frac{16}{4} = 4
   \]

2. **Divide the powers of \( x \)**:
   Apply the rule \( \frac{x^a}{x^b} = x^{a-b} \):
   \[
   \frac{x^5}{x^2} = x^{5-2} = x^3
   \]

3. **Divide the powers of \( y \)**:
   Similarly, apply \( \frac{y^a}{y^b} = y^{a-b} \):
   \[
   \frac{y^7}{y^3} = y^{7-3} = y^4
   \]

### Final result:
\[
\frac{16x^5y^7}{4x^2y^3} = 4x^3y^4
\]

The resulting expression is \( 4x^3y^4 \).

Would you like more details on any part of this explanation, or further questions?

Here are five related questions to deepen your understanding:

1. How do you simplify expressions with negative exponents?
2. What is the rule for dividing two monomials with the same base?
3. How can you apply these division rules to more complex polynomials?
4. What happens when the exponents in the denominator are larger than in the numerator?
5. How would the result change if there was an additional variable in the expression?

**Tip**: Always subtract the exponents of like bases when dividing powers, and remember to simplify the coefficients first!

Divide the monomial 16x^5y^7 by the monomial 4x^2y^3. What is the resulting expression?

Learn how to divide the monomial 16x^5y^7 by 4x^2y^3 using the rules of exponents and basic division. This problem covers key concepts of monomial division and exponent rules, suitable for Grades 8-10.

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