https://r2.erweima.ai/mathbot/image/1726326486274vha1rwld.jpg

Let's solve the divisions provided in the image:

**Part a**: \( 15x^3 \div (-3x^2) \)
\[ \frac{15x^3}{-3x^2} = -5x \]
We divide the coefficients (15 by -3 to get -5) and subtract the exponents of \( x \) (3 - 2 to get 1).

**Part b**: \( 18a^6b^3 \div 6a^4b \)
\[ \frac{18a^6b^3}{6a^4b} = 3a^{6-4}b^{3-1} = 3a^2b^2 \]
Here, we divide the numerical coefficients (18 by 6 to get 3) and subtract the exponents for \( a \) (6 - 4 to get 2) and for \( b \) (3 - 1 to get 2).

Would you like to explore more details or have questions on how these calculations are done?

Here are some additional questions you might consider:
1. What would be the result if the negative sign in part a was associated with the entire fraction instead of just the denominator?
2. How would the result change in part b if the exponent of \( b \) in the denominator was \( b^2 \) instead of \( b \)?
3. Can you simplify the expression \( \frac{36x^4y^2}{9xy} \)?
4. What are the general rules for dividing terms with exponents?
5. Could you try solving \( \frac{24x^5y}{-3xy^4} \) and explain each step?

Tip: When dividing terms with exponents, remember to subtract the exponents if the bases are the same. This applies to any variables involved.

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

Learn how to divide monomials with exponents and negative coefficients through the problems 15x^3 ÷ (-3x^2) and 18a^6b^3 ÷ 6a^4b. This tutorial provides a detailed step-by-step solution covering algebraic concepts of exponent subtraction and coefficient division. Suitable for students in Grades 7-9.

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