Find the following product.
$ \left(-\frac{1}{27} a^{2} b^{2}\right) \times\left(\frac{9}{2} a^{3} b^{2} c^{2}\right) $

Given:

\( \left(-\frac{1}{27} a^{2} b^{2}\right) \times\left(\frac{9}{2} a^{3} b^{2} c^{2}\right) \)

To do:

We have to find the given product.

Solution:

$(-\frac{1}{27} a^{2} b^{2}) \times(\frac{9}{2} a^{3} b^{2} c^{2})=-\frac{1}{27} \times \frac{9}{2} \times a^{2} \times a^{3} \times b^{2} \times b^{2} \times c^{2}$

$=-\frac{1}{3 \times 2} \times a^{2+3} \times b^{2+2} \times c^{2}$

$=-\frac{1}{6} a^{5} b^{4} c^{2}$