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The image you've uploaded contains a set of math problems related to simplifying algebraic expressions and operations. Let me extract the details and solve a few of them for you.

Here are the extracted problems and their solutions:

### Problems and Solutions:

1. **Problem 13:** Simplify \(\frac{a \cdot a \cdot a}{a^2}\).
   
   **Solution:**
   \[
   \frac{a \cdot a \cdot a}{a^2} = \frac{a^3}{a^2} = a^{3-2} = a
   \]

2. **Problem 14:** Simplify \(\frac{b^3 \cdot b}{b \cdot b \cdot b}\).

   **Solution:**
   \[
   \frac{b^3 \cdot b}{b \cdot b \cdot b} = \frac{b^4}{b^3} = b^{4-3} = b
   \]

3. **Problem 15:** Simplify \(\frac{x^2 \cdot x}{1000}\).

   **Solution:**
   \[
   \frac{x^2 \cdot x}{1000} = \frac{x^3}{1000}
   \]

4. **Problem 16:** Simplify \(\frac{x \cdot y}{x \cdot 1000}\).

   **Solution:**
   \[
   \frac{x \cdot y}{x \cdot 1000} = \frac{y}{1000}
   \]

5. **Problem 17:** Simplify \(\frac{m \cdot n \cdot 1000}{m \cdot n}\).

   **Solution:**
   \[
   \frac{m \cdot n \cdot 1000}{m \cdot n} = 1000
   \]

6. **Problem 18:** Simplify \(\frac{p \cdot q \cdot r}{p \cdot 1000}\).

   **Solution:**
   \[
   \frac{p \cdot q \cdot r}{p \cdot 1000} = \frac{q \cdot r}{1000}
   \]

7. **Problem 19:** Simplify \(\frac{a \cdot b \cdot c \cdot 1000}{a \cdot b \cdot c}\).

   **Solution:**
   \[
   \frac{a \cdot b \cdot c \cdot 1000}{a \cdot b \cdot c} = 1000
   \]

8. **Problem 20:** Simplify \(\frac{m \cdot m \cdot n \cdot n}{m \cdot n \cdot 1000}\).

   **Solution:**
   \[
   \frac{m \cdot m \cdot n \cdot n}{m \cdot n \cdot 1000} = \frac{m \cdot n}{1000}
   \]

9. **Problem 21:** Simplify \(\frac{m^2 \cdot n^2}{m \cdot n \cdot 1000}\).

   **Solution:**
   \[
   \frac{m^2 \cdot n^2}{m \cdot n \cdot 1000} = \frac{m^{2-1} \cdot n^{2-1}}{1000} = \frac{m \cdot n}{1000}
   \]

10. **Problem 22:** Simplify \(\frac{a \cdot b \cdot c \cdot d \cdot e \cdot f \cdot g \cdot h \cdot i}{1000}\).

    **Solution:**
    \[
    \frac{a \cdot b \cdot c \cdot d \cdot e \cdot f \cdot g \cdot h \cdot i}{1000}
    \]

Let me know if you would like further details on any specific problem or have any additional questions!

### Related Questions:

1. How do you simplify expressions with variables in the numerator and denominator?
2. What are the rules of exponents used in simplifying algebraic fractions?
3. How do you simplify expressions involving multiplication and division of variables?
4. What techniques can you use to factor expressions before simplifying?
5. How does simplifying an expression change when dealing with constants like \(1000\)?

**Tip:** When simplifying fractions involving variables, always look for common factors in the numerator and denominator to cancel out!

The image contains algebraic simplifications and operations, such as simplifying expressions with exponents and variables.

This page explains how to simplify algebraic expressions using exponent rules and variable multiplication and division. Learn step-by-step solutions for problems involving algebraic fractions, suitable for students in Grades 6-8.

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