Question

Find each of the following product:
$(-7xy)\times \left(\frac{1}{4}{x}^{2}yz\right)$

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:

$$\begin{gathered} \left(-7xy\right)\times \left(\frac{1}{4}{x}^{2}yz\right) \\ =\left(-7\times \frac{1}{4}\right)\times \left(x\times x^2\right)\times \left(y\times y\right)\times z \\ =\left(-7\times \frac{1}{4}\right)\times \left(x^{1+2}\right)\times \left(y^{1+1}\right)\times z \\ =-\frac{7}{4}{x}^3{y}^{2}z \end{gathered}$$

Thus, the answer is $-\frac{7}{4}{x}^3{y}^{2}z$.