To simplify the expression \((3a^{-3})(5a^{2})\), we can do the following:
- Multiply the constant coefficients: \(3 \times 5 = 15\).
- Combine the powers of \(a\): \(a^{-3} \times a^{2} = a^{-3 + 2} = a^{-1}\).
So we can rewrite the entire expression as: \[ 15a^{-1} \]
This can also be expressed as: \[ \frac{15}{a} \]
Now, let's evaluate your responses:
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3×5×a×aa×a×a - This expression appears to be incorrect as it does not accurately represent the multiplication and powers involved.
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15a - This is incorrect as the simplified expression is \(15a^{-1}\) or \(\frac{15}{a}\), not \(15a\).
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3×a×a×a×5×a×a - This simplifies to \(15a^{5}\), which is also incorrect as it eliminates the negative exponent incorrectly.
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15a - As mentioned before, this is incorrect for the same reasons.
From this analysis, the correct equivalent expression for \((3a^{-3})(5a^{2})\) is:
- \(\frac{15}{a}\)
None of the provided options correctly reflect this equivalent expression.