The expression you provided is \( e^{\frac{2}{3} \ln(x^2 + 4)} \). This can be simplified using properties of logarithms and exponents.

### Steps for Simplification:

1. **Exponent and Logarithm Relationship**: Recall that \( e^{\ln(a)} = a \). In this case, we have \( e^{\frac{2}{3} \ln(x^2 + 4)} \).

2. **Move the exponent inside the logarithm**: Using the rule \( a \ln(b) = \ln(b^a) \), we can rewrite the expression:
   \[
   e^{\frac{2}{3} \ln(x^2 + 4)} = e^{\ln((x^2 + 4)^{\frac{2}{3}})}
   \]

3. **Exponentiating cancels the logarithm**: Since \( e^{\ln(a)} = a \), we can simplify further:
   \[
   e^{\ln((x^2 + 4)^{\frac{2}{3}})} = (x^2 + 4)^{\frac{2}{3}}
   \]

Thus, the simplified form of the expression is:
\[
(x^2 + 4)^{\frac{2}{3}}
\]

Would you like more details or have any questions?

### Related Questions:
1. How do we simplify expressions involving natural logarithms and exponents in general?
2. Can you show the steps for solving logarithmic equations?
3. What are the rules for combining logarithms and exponents?
4. How do we differentiate or integrate expressions like \( \ln(x^2 + 4) \)?
5. How do we solve equations involving fractional exponents?

**Tip**: Always look for logarithmic and exponential identities when simplifying complex expressions.

Learn how to simplify the expression e^(2/3)(ln(x^2 + 4)) using logarithmic and exponential identities. This problem involves key concepts like exponents, logarithms, and algebraic manipulation, suitable for high school students in Grades 10-12.

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