To simplify the expression \( 3e^3 + \frac{1}{2}e^3 + 1 \), follow these steps:

1. **Combine like terms**: Both \( 3e^3 \) and \( \frac{1}{2}e^3 \) are like terms because they both contain \( e^3 \).

2. **Add the coefficients**:
   \[
   3 + \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{7}{2}
   \]
   So, the expression becomes:
   \[
   \frac{7}{2}e^3 + 1
   \]

Thus, the simplified expression is:
\[
\frac{7}{2}e^3 + 1
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you simplify expressions with different exponential terms?
2. What is the general process for combining like terms?
3. Can you explain how to add fractions with different denominators?
4. What does the constant \( e \) represent in mathematics?
5. How would the expression change if there was a subtraction instead of addition?

**Tip:** When combining like terms, always focus on the coefficients and ensure they have the same variable part before performing arithmetic operations.

Learn how to simplify the expression 3e^3 + 1/2e^3 + 1 with detailed steps. This problem involves combining like terms in exponential expressions and adding fractions. Suitable for high school students learning algebra and exponential functions.

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