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:

$(-7 x y) \times\left(\frac{1}{4} x^{2} y z\right)$

$=\left(-7 \times \frac{1}{4}\right) \times\left(x \times x^{2}\right) \times(y \times y) \times z$

$=\left(-7 \times \frac{1}{4}\right) \times\left(x^{1+2}\right) \times\left(y^{1+1}\right) \times z$

$=-\frac{7}{4} x^{3} y^{2} z$

Thus, the answer is $-\frac{7}{4} x^{3} y^{2} z$.