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The expression in the image involves fractions of polynomials in several variables (e.g., \( z \), \( x \), \( s \)), and each term contains both numerical and variable components. The operations include multiplication, exponents, and division.

Let's break down and simplify this expression:

1. **Numerators and Denominators**: Each part of the expression has numerators and denominators with both constant coefficients and terms involving variables raised to different powers.
   
2. **Multiplication of Fractions**: When multiplying fractions, we multiply the numerators together and the denominators together. The same applies to the variables and their exponents (using exponent rules).

3. **Exponent Rules**: The variables in the numerators and denominators follow rules of exponents:
   - When multiplying variables of the same base, we add the exponents: \( z^a \cdot z^b = z^{a+b} \).
   - When dividing variables of the same base, we subtract the exponents: \( \frac{z^a}{z^b} = z^{a-b} \).

4. **Combining Powers**: Any fractional exponents (like \( \frac{8}{4} \), \( \frac{-3}{4} \), etc.) apply to both the constants and the variables.

### I will proceed by simplifying the full expression using these principles:

I will calculate step-by-step and give the detailed answer.The simplified form of the given expression is:

\[
-2.31818181818182 \cdot \frac{x^{-45} \cdot s^{-33.5}}{z^{28}}
\]

This means the entire expression reduces to a constant coefficient multiplied by variables \(x\), \(s\), and \(z\) raised to negative powers.

Would you like further clarification on any part of the process or details on specific steps?

Here are 5 related questions you might find helpful:
1. How are fractional exponents handled in multiplication and division?
2. What happens when variables with negative exponents are involved in a fraction?
3. How can we convert the final result into positive exponents?
4. What role do constants play in this type of expression simplification?
5. How would the result change if we altered one of the coefficients in the original expression?

**Tip:** When simplifying expressions involving powers and fractions, always apply exponent rules systematically to avoid errors.

Simplify the given complex fraction involving multiple variables and exponents.

Learn how to simplify a complex fraction involving multiple variables and exponents with step-by-step guidance on applying algebraic rules. Suitable for advanced high school students in Grades 11-12.

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