Question

Find each of the following product:

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

Answer 1

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:

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

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

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

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

Thus, the answer is \[- \frac{1}{6} a^5 b^4 c^2\].