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Question
Find each of the following product:
(−5a) × (−10a2) × (−2a3)
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Solution
To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, i.e., \[a^m \times a^n = a^{m + n}\]
We have:
\[\left( - 5a \right) \times \left( - 10 a^2 \right) \times \left( - 2 a^3 \right)\]
\[ = \left\{ \left( - 5 \right) \times \left( - 10 \right) \times \left( - 2 \right) \right\} \times \left( a \times a^2 \times a^3 \right)\]
\[ = \left\{ \left( - 5 \right) \times \left( - 10 \right) \times \left( - 2 \right) \right\} \times \left( a^{1 + 2 + 3} \right)\]
\[ = - 100 a^6 \]
Thus, the answer is \[- 100 a^6\].
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