Question

Find each of the following product:
$\left(\frac{-24}{25}{x}^{3}z\right)\times \left(-\frac{15}{16}x{z}^{2}y\right)$

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:

$$\begin{gathered} \left(-\frac{24}{25}{x}^{3}z\right)\times \left(-\frac{15}{16}x{z}^{2}y\right) \\ =\left\{\left(-\frac{24}{25}\right)\times \left(-\frac{15}{16}\right)\right\}\times \left(x^3\times x\right)\times \left(z\times z^2\right)\times y \\ =\left\{\left(-\frac{24}{25}\right)\times \left(-\frac{15}{16}\right)\right\}\times \left(x^{3+1}\right)\times \left(z^{1+2}\right)\times y \end{gathered}$$
$=\frac{9}{10}{x}^{4}y{z}^3$

Thus, the answer is $\frac{9}{10}{x}^{4}y{z}^3$.