Question

Find each of the following product:
$\left(-\frac{1}{27}{a}^2{b}^2\right)\times \left(\frac{9}{2}{a}^3{b}^2{c}^2\right)$

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:

$$\begin{gathered} \left(-\frac{1}{27}{a}^2{b}^2\right)\times \left(\frac{9}{2}{a}^3{b}^2{c}^2\right) \\ =\left(-\frac{1}{27}\times \frac{9}{2}\right)\times \left(a^2\times a^3\right)\times \left(b^2\times b^2\right)\times c^2 \\ =\left(-\frac{1}{27}\times \frac{9}{2}\right)\times \left(a^{2+3}\right)\times \left(b^{2+2}\right)\times c^2 \\ =-\frac{1}{6}{a}^5{b}^4{c}^2 \end{gathered}$$

Thus, the answer is $-\frac{1}{6}{a}^5{b}^4{c}^2$.