Question

Find each of the following product:
(7ab) × (−5ab²c) × (6abc²)

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:

\[\left( 7ab \right) \times \left( - 5a b^2 c \right) \times \left( 6ab c^2 \right)\]

\[ = \left\{ 7 \times \left( - 5 \right) \times 6 \right\} \times \left( a \times a \times a \right) \times \left( b \times b^2 \times b \right) \times \left( c \times c^2 \right)\]

\[ = \left\{ 7 \times \left( - 5 \right) \times 6 \right\} \times \left( a^{1 + 1 + 1} \right) \times \left( b^{1 + 2 + 1} \right) \times \left( c^{1 + 2} \right)\]

\[ = - 210 a^3 b^4 c^3\]

Thus, the answer is \[- 210 a^3 b^4 c^3\] .