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Simplify then express the expression in exponential form which bases written in ascending order

The expression provided in the image is:

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

Let's simplify the expression and express it in exponential form with bases in ascending order.

### Step 1: Simplify the constants (3's)
Use the properties of exponents to simplify the terms with the base \(3\):

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

### Step 2: Simplify the \(x\) terms
Simplify the terms involving \(x\):

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

### Step 3: Combine the simplified terms
Now, combine the simplified results:

\[
3^2 \cdot x^2
\]

### Final Answer
The simplified expression in exponential form with bases written in ascending order is:

\[
3^2 \cdot x^2
\]

Would you like any further details or have any questions?

### Related Questions:
1. How would the expression change if the exponent of \(x\) in the numerator was 6 instead of 5?
2. What if the base \(3\) in the numerator had an exponent of 4 instead of 5?
3. Can you generalize the process for simplifying similar expressions with different bases?
4. What are the implications of raising the entire expression to another power?
5. How does the order of operations affect the simplification process?

**Tip:** Always arrange the terms in ascending order of the base before finalizing the simplified expression, especially when required by the problem.

Learn how to simplify and express an expression with exponents in ascending order. This problem involves using properties of exponents to simplify terms and arranging bases in ascending order in the final expression. Suitable for Grades 9-12 students seeking to master exponent manipulation.

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