https://r2.erweima.ai/mathbot/image/17263256684250843qru6.jpg

Let's work through the division problems from the image.

### a. \( \frac{15x^3}{-3x^2} \)

1. Divide the coefficients:
   \[
   \frac{15}{-3} = -5
   \]

2. For the exponents of \(x\), subtract the exponents:
   \[
   x^{3 - 2} = x^1 = x
   \]

Thus, the result is:
\[
-5x
\]

---

### b. \( \frac{18a^6b^2}{6a^4b} \)

1. Divide the coefficients:
   \[
   \frac{18}{6} = 3
   \]

2. For the exponents of \(a\), subtract the exponents:
   \[
   a^{6 - 4} = a^2
   \]

3. For the exponents of \(b\), subtract the exponents:
   \[
   b^{2 - 1} = b
   \]

Thus, the result is:
\[
3a^2b
\]

---

### Final Results:

a. \( -5x \)

b. \( 3a^2b \)

Would you like further clarification or more details?

Here are five related questions for deeper understanding:
1. How would you handle divisions with negative exponents?
2. What happens if the exponents in the numerator are smaller than in the denominator?
3. Can you perform the same operation with fractional exponents?
4. How would the result change if there were additional variables, like \(y\), in the division?
5. What role does the sign (positive or negative) play in these types of division problems?

**Tip**: When dividing terms with the same base, always subtract the exponents of the base!

Realiza las siguientes divisiones: a. 15x^3 ÷ (-3x^2) b. 18a^6b^2 ÷ 6a^4b

Learn how to solve polynomial divisions like 15x^3 ÷ (-3x^2) and 18a^6b^2 ÷ 6a^4b with detailed explanations. This guide covers key concepts in algebra, including exponent rules and division of monomials. Ideal for students in Grades 7-9.

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