https://file.aiquickdraw.com/mathbot/file/17249700288453yepv2uv.jpg

To simplify the expression given in the image, let's break it down step by step.

The expression is:

\[
\frac{3^5 \cdot 3x^5}{3^4 \cdot x^3} \cdot \frac{1}{x^3}
\]

### Step 1: Simplify the constants
The constants involving \(3\) can be simplified using the properties of exponents. 

\[
\frac{3^5 \cdot 3}{3^4} = \frac{3^{5+1}}{3^4} = \frac{3^6}{3^4} = 3^{6-4} = 3^2 = 9
\]

### Step 2: Simplify the \(x\) terms
Next, simplify the \(x\) terms:

\[
\frac{x^5}{x^3} = x^{5-3} = x^2
\]

But there's another \(x^3\) in the denominator:

\[
\frac{x^2}{x^3} = x^{2-3} = x^{-1} = \frac{1}{x}
\]

### Step 3: Combine the simplified terms
Now, combine all the simplified parts:

\[
\frac{3^5 \cdot 3x^5}{3^4 \cdot x^3} \cdot \frac{1}{x^3} = 9 \cdot \frac{1}{x} = \frac{9}{x}
\]

So, the simplified expression is:

\[
\frac{9}{x}
\]

Would you like any further details or have any questions?

### Related Questions:
1. How would the result change if the numerator had an additional factor of \(x^2\)?
2. What is the general rule for simplifying expressions involving powers of variables and constants?
3. How do negative exponents affect the simplification process?
4. Can the same process be used to simplify fractions with different bases?
5. What is the significance of the exponent zero in such expressions?

**Tip:** Always simplify constants and variable terms separately, then combine the results.

Learn how to simplify an expression involving exponents and fractions step-by-step with a detailed solution. This problem covers key concepts in algebra, including exponent properties and fraction simplification techniques. Suitable for students in Grades 7-9.

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