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Simplify the expression so there is only one positive power for each base.
[tex]\[ 2.7^{-3} \cdot 3.8^2 \cdot 2.7^4 \cdot 3.8^3 \][/tex]

A. [tex]\[2.7^7 \cdot 3.8^5\][/tex]

B. [tex]\[2.7^{-7} \cdot 3.8^5\][/tex]

C. [tex]\[2.7 \cdot 3.8^5\][/tex]

D. [tex]\[2.7 \cdot 3.8\][/tex]

E. [tex]\[2.7^7 \cdot 3.8\][/tex]

Sagot :

GinnyAnswer
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]
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