Question

Express each of the following product as a monomials and verify the result for x = 1, y = 2:
$\left(-\frac{4}{7}{a}^{2}b\right)\times \left(-\frac{2}{3}{b}^{2}c\right)\times \left(-\frac{7}{6}{c}^{2}a\right)$

Answer 1

To multiply algebraic expressions, we use commutative and associative laws along with the laws of indices, i.e.,​ $a^m\times a^n=a^{m+n}$.

We have:

$$\begin{gathered} \left(-\frac{4}{7}{a}^{2}b\right)\times \left(-\frac{2}{3}{b}^{2}c\right)\times \left(-\frac{7}{6}{c}^{2}a\right) \\ =\left\{\left(-\frac{4}{7}\right)\times \left(-\frac{2}{3}\right)\times \left(-\frac{7}{6}\right)\right\}\times \left(a^2\times a\right)\times \left(b\times b^2\right)\times \left(c\times c^2\right) \\ =\left\{\left(-\frac{4}{7}\right)\times \left(-\frac{2}{3}\right)\times \left(-\frac{7}{6}\right)\right\}\times \left(a^{2+1}\right)\times \left(b^{1+2}\right)\times \left(c^{1+2}\right) \\ =-\frac{4}{9}{a}^3{b}^3{c}^3 \end{gathered}$$

$\because$ The expression doesn't consist of the variables x and y.

$\therefore$ The result cannot be verified for x = 1 and y = 2.

Thus, the answer is $-\frac{4}{9}{a}^3{b}^3{c}^3$.