Find the following product.
$\frac{1}{2} x y \times \frac{2}{3} x^{2} y z^{2}$

Given:

$\frac{1}{2} x y \times \frac{2}{3} x^{2} y z^{2}$

To do:

We have to find the given product.

Solution:

$\frac{1}{2} x y \times \frac{2}{3} x^{2} y z^{2}=[\frac{1}{2}\times\frac{2}{3}]\times(xy \times x^2yz^2)$

$=\frac{1}{3}\times x^{1+2}\times y^{1+1}\times z^2$

$=\frac{1}{3}x^3y^2z^2$