Question

Find each of the following product:
(−5a) × (−10a²) × (−2a³)

Answer 1

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 \[- 100 a^6\].