Question

Find each of the following product:

\[\left( - \frac{2}{7} a^4 \right) \times \left( - \frac{3}{4} a^2 b \right) \times \left( - \frac{14}{5} b^2 \right)\]

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:

\[\left( - \frac{2}{7} a^4 \right) \times \left( - \frac{3}{4} a^2 b \right) \times \left( - \frac{14}{5} b^2 \right)\]

\[ = \left\{ \left( - \frac{2}{7} \right) \times \left( - \frac{3}{4} \right) \times \left( - \frac{14}{5} \right) \right\} \times \left( a^4 \times a^2 \right) \times \left( b \times b^2 \right)\]

\[ = \left\{ - \left( \frac{2}{7} \times \frac{3}{4} \times \frac{14}{5} \right) \right\} \times a^{4 + 2} \times b^{1 + 2} \]

\[ = \left\{ - \left( \frac{2}{7} \times \frac{3}{4_2} \times \frac{{14}^{2^1}}{5} \right) \right\} \times a^6 \times b^3 \]

\[ = - \frac{3}{5} a^6 b^3\]

Thus, the answer is \[- \frac{3}{5} a^6 b^3\].