Question

Find each of the following product:
$\left(\frac{4}{3}{u}^{2}vw\right)\times \left(-5uv{w}^2\right)\times \left(\frac{1}{3}{v}^{2}wu\right)$

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:

$$\begin{gathered} \left(\frac{4}{3}{u}^{2}vw\right)\times \left(-5uv{w}^2\right)\times \left(\frac{1}{3}{v}^{2}wu\right) \\ =\left\{\frac{4}{3}\times \left(-5\right)\times \frac{1}{3}\right\}\times \left(u^2\times u\times u\right)\times \left(v\times v\times v^2\right)\times \left(w\times w^2\times w\right) \\ =\left\{\frac{4}{3}\times \left(-5\right)\times \frac{1}{3}\right\}\times \left(u^{2+1+1}\right)\times \left(v^{1+1+2}\right)\times \left(w^{1+2+1}\right) \\ =-\frac{20}{9}{u}^4{v}^4{w}^4 \end{gathered}$$

Thus, the answer is $-\frac{20}{9}{u}^4{v}^4{w}^4$.