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03/14/2024 · Elementary School
Simplify. Give your answers as positive exponents. \( a^{5} \cdot a^{-2} \) A. \( \frac{a^{2}}{a^{2}} \) B. \( a^{3} \) C. \( \frac{a^{5}}{a^{2}} \) D. \( a^{2} \)
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Step-by-step Solution
To simplify \( a^{5} \cdot a^{-2} \), we can use the property of exponents that states \( a^{m} \cdot a^{n} = a^{m+n} \).
Applying this property:
\[
a^{5} \cdot a^{-2} = a^{5 + (-2)} = a^{5 - 2} = a^{3}
\]
Thus, the simplified expression is \( a^{3} \).
The correct answer is:
**B. \( a^{3} \)**
Quick Answer
B. \( a^{3} \)
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