To simplify the expression \(2.7^{-3} \cdot 3.8^2 \cdot 2.7^4 \cdot 3.8^3\), follow these steps:
1. Combine the Exponents for Similar Bases:
- For the base \(2.7\), you have the terms \(2.7^{-3}\) and \(2.7^4\).
- For the base \(3.8\), you have the terms \(3.8^2\) and \(3.8^3\).
2. Simplify the Exponents:
- For \(2.7\), add the exponents: \(-3 + 4\).
- This yields \(1\).
- For \(3.8\), add the exponents: \(2 + 3\).
- This yields \(5\).
3. Rewrite the Expression with Simplified Exponents:
- The simplified expression is \(2.7^1 \cdot 3.8^5\).
4. Identify the Correct Answer:
- The simplified form of the expression is \(2.7 \cdot 3.8^5\).
- Among the options given, this corresponds to option C.
Thus, the correct answer is:
C. [tex]\(2.7 \cdot 3.8^5\)[/tex]
