Find each of the following product:

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:

$(0.5 x) \times\left(\frac{1}{3} x y^{2} z^{4}\right) \times\left(24 x^{2} y z\right)$

$=\left(0.5 \times \frac{1}{3} \times 24\right) \times\left(x \times x \times x^{2}\right) \times\left(y^{2} \times y\right) \times\left(z^{4} \times z\right)$

$=\left(0.5 \times \frac{1}{3} \times 24\right) \times\left(x^{1+1+2}\right) \times\left(y^{2+1}\right) \times\left(z^{4+1}\right)$

$=4 x^{4} y^{3} z^{5}$

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