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:

$\left(\frac{4}{3} p q^{2}\right) \times\left(-\frac{1}{4} p^{2} r\right) \times\left(16 p^{2} q^{2} r^{2}\right)$

$=\left\{\frac{4}{3} \times\left(-\frac{1}{4}\right) \times 16\right\} \times\left(p \times p^{2} \times p^{2}\right) \times\left(q^{2} \times q^{2}\right) \times\left(r \times r^{2}\right)$

$=\left\{\frac{4}{3} \times\left(-\frac{1}{4}\right) \times 16\right\} \times\left(p^{1+2+2}\right) \times\left(q^{2+2}\right) \times\left(r^{1+2}\right)$

$=-\frac{16}{3} p^{5} q^{4} r^{3}$

Thus, the answer is $-\frac{1}{3} p^{5} q^{4} r^{3}$.