Question

Find each of the following product:
$\left(-\frac{7}{5}x{y}^{2}z\right)\times \left(\frac{13}{3}{x}^{2}y{z}^2\right)$

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:

$$\begin{gathered} \left(-\frac{7}{5}x{y}^{2}z\right)\times \left(\frac{13}{3}{x}^{2}y{z}^2\right) \\ =\left(-\frac{7}{5}\times \frac{13}{3}\right)\times \left(x\times x^2\right)\times \left(y^2\times y\right)\times \left(z\times z^2\right) \\ =\left(-\frac{7}{5}\times \frac{13}{3}\right)\times \left(x^{1+2}\right)\times \left(y^{2+1}\right)\times \left(z^{1+2}\right) \\ =-\frac{91}{15}{x}^3{y}^3{x}^3 \end{gathered}$$

Thus, the answer is $-\frac{91}{15}{x}^3{y}^3{x}^3$.