Practice worksheet for simplifying division of monomials.

It looks like you've uploaded a worksheet titled "Dividing by Monomials" with a series of algebraic expressions that need to be simplified. The instructions say: *"Simplify. Assume that no denominator is equal to zero."*

Since I can't see the actual image, I’ll help you solve this type of problem based on the typical format of such worksheets.

Let’s assume the problems are similar to common dividing monomials exercises. Here's how to approach them:

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🔧 General Rule for Dividing Monomials

When dividing two monomials (single-term algebraic expressions), follow these steps:

1. Divide the coefficients (numbers).
2. Subtract the exponents of like bases using the rule:
$$
\frac{a^m}{a^n} = a^{m-n}
$$
3. Keep any variables that don’t appear in both numerator and denominator.

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✔ Example Problem

Let’s suppose one of the problems is:

$$
\frac{12x^5y^3}{4x^2y}
$$

#### Step-by-step solution:

1. Divide the coefficients:
$$
\frac{12}{4} = 3
$$

2. Subtract exponents of like bases:
- For $ x $: $ x^{5-2} = x^3 $
- For $ y $: $ y^{3-1} = y^2 $

3. Combine:
$$
3x^3y^2
$$

✔ Final Answer: $ 3x^3y^2 $

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Now, let me go through a few more example problems you might have on your sheet (since I can’t see the actual image):

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📌 Example Problems & Solutions

1. $ \frac{15a^4b^2}{5a^2b} $

- Coefficients: $ \frac{15}{5} = 3 $
- $ a^{4-2} = a^2 $
- $ b^{2-1} = b $
- Answer: $ 3a^2b $

2. $ \frac{-8x^6y^2}{-4x^3y} $

- Coefficients: $ \frac{-8}{-4} = 2 $
- $ x^{6-3} = x^3 $
- $ y^{2-1} = y $
- Answer: $ 2x^3y $

3. $ \frac{20m^3n^5}{10m^2n^3} $

- $ \frac{20}{10} = 2 $
- $ m^{3-2} = m $
- $ n^{5-3} = n^2 $
- Answer: $ 2mn^2 $

4. $ \frac{9p^7q^4}{3p^5q} $

- $ \frac{9}{3} = 3 $
- $ p^{7-5} = p^2 $
- $ q^{4-1} = q^3 $
- Answer: $ 3p^2q^3 $

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⚠️ Common Mistakes to Avoid

- Forgetting to subtract exponents.
- Not simplifying coefficients.
- Misapplying negative signs.
- Leaving variables in the denominator when they can be canceled.

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✔ Tips

- Always write out each step clearly.
- Cancel common factors first if possible.
- Remember: any variable without an exponent has an implied exponent of 1.

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If you can describe or list the specific problems from your worksheet (e.g., "Problem 1: $ \frac{18x^4y^3}{6x^2y} $" etc.), I can solve them exactly as they appear.

Alternatively, if you can upload the image again or paste the text, I’ll provide full solutions for all the problems on the page.