Question

Find each of the following product:
$\frac{1}{4}xy\times \frac{2}{3}{x}^{2}y{z}^2$

Answer 1

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

We have:

$$\begin{gathered} \frac{1}{4}xy\times \frac{2}{3}{x}^{2}y{z}^2 \\ =\left(\frac{1}{4}\times \frac{2}{3}\right)\times \left(x\times x^2\right)\times \left(y\times y\right)\times z^2 \\ =\left(\frac{1}{4}\times \frac{2}{3}\right)\times \left(x^{1+2}\right)\times \left(y^{1+1}\right)\times z^2 \\ =\frac{1}{6}{x}^3{y}^2{z}^2 \end{gathered}$$

Thus, the answer is $\frac{1}{6}{x}^3{y}^2{z}^2$.