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The expression you provided is:

\[
\frac{54w^2x^5}{9w^3x^5}
\]

### Step-by-step Simplification:

1. **Simplify the constants**:  
   \[
   \frac{54}{9} = 6
   \]

2. **Simplify the powers of \( w \)**:
   \[
   \frac{w^2}{w^3} = w^{2-3} = w^{-1} = \frac{1}{w}
   \]

3. **Simplify the powers of \( x \)**:  
   Since \( x^5 \) is present in both the numerator and the denominator, they cancel out:
   \[
   \frac{x^5}{x^5} = 1
   \]

Now, putting it all together:
\[
\frac{54w^2x^5}{9w^3x^5} = 6 \times \frac{1}{w} \times 1 = \frac{6}{w}
\]

### Final Simplified Expression:
\[
\frac{6}{w}
\]

Would you like any further details or clarifications?

Here are some related questions to expand on this topic:

1. How do you simplify expressions involving negative exponents?
2. What are the laws of exponents that apply to division?
3. Can the final expression \(\frac{6}{w}\) be simplified further for any specific values of \(w\)?
4. How do you handle simplifying terms with different variables in the numerator and denominator?
5. How can this simplification be applied to more complex algebraic fractions?

**Tip**: Always start by simplifying constants and variables separately before combining them in your final answer.

Simplify the expression: (54w^2x^5) / (9w^3x^5).

Learn how to simplify the algebraic expression 54w^2x^5 / 9w^3x^5 using exponent rules. This step-by-step guide explains how to simplify constants and powers, making it ideal for students in Grades 8-10.

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