Question

Find each of the following product:
$\left(0.5x\right)\times \left(\frac{1}{3}x{y}^2{z}^4\right)\times \left(24x^{2}yz\right)$

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:
$$\begin{gathered} \left(0.5x\right)\times \left(\frac{1}{3}x{y}^2{z}^4\right)\times \left(24x^{2}yz\right) \\ =\left(0.5\times \frac{1}{3}\times 24\right)\times \left(x\times x\times x^2\right)\times \left(y^2\times y\right)\times \left(z^4\times z\right) \\ =\left(0.5\times \frac{1}{3}\times 24\right)\times \left(x^{1+1+2}\right)\times \left(y^{2+1}\right)\times \left(z^{4+1}\right) \\ =4x^4{y}^3{z}^5 \end{gathered}$$

Thus, the answer is $4x^4{y}^3{z}^5$.