Let's expand the expression \((3^{2x+3})(3^{3x-2})\).

When you multiply terms with the same base, you add their exponents. Therefore, the expression simplifies as follows:

\[
(3^{2x+3})(3^{3x-2}) = 3^{(2x+3) + (3x-2)}
\]

Now, combine the exponents:

\[
(2x + 3) + (3x - 2) = 2x + 3x + 3 - 2 = 5x + 1
\]

So, the simplified expression is:

\[
3^{5x+1}
\]

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you add exponents when multiplying powers with the same base?
2. What is the significance of the base in exponential expressions?
3. How do you solve equations involving exponents like \(3^{5x+1} = 81\)?
4. What are the common mistakes to avoid when working with exponents?
5. How do you apply the properties of exponents in complex algebraic expressions?

**Tip:** When dealing with exponential expressions, always double-check that you're adding or subtracting exponents correctly according to the operation (multiplication or division).

Learn how to expand and simplify the expression (32x+3)(33x-2) step-by-step with detailed explanations. This problem involves exponents and multiplying powers with the same base. Suitable for students in Grades 9-12.

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