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:

$$\begin{gathered} \left(-\frac{2}{7}{a}^4\right)\times \left(-\frac{3}{4}{a}^{2}b\right)\times \left(-\frac{14}{5}{b}^2\right) \\ =\left\{\left(-\frac{2}{7}\right)\times \left(-\frac{3}{4}\right)\times \left(-\frac{14}{5}\right)\right\}\times \left(a^4\times a^2\right)\times \left(b\times b^2\right) \\ =\left\{-\left(\frac{2}{7}\times \frac{3}{4}\times \frac{14}{5}\right)\right\}\times a^{4+2}\times b^{1+2} \\ =\left\{-\left(\frac{\cancel{2}}{\cancel{7}}\times \frac{3}{{\cancel{4}}_{\cancel{2}}}\times \frac{{\cancel{14}}^{{\cancel{2}}^1}}{5}\right)\right\}\times a^6\times b^3 \\ =-\frac{3}{5}{a}^6{b}^3 \end{gathered}$$

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