Question

Find each of the following product: 

\[\frac{1}{4}xy \times \frac{2}{3} x^2 y z^2\]

Answer 1

To multiply algebraic expressions, we use commutative and associative laws along with the the law of indices, that is,  \[a^m \times a^n = a^{m + n}\].

We have:

\[\frac{1}{4}xy \times \frac{2}{3} x^2 y z^2 \]

\[ = \left( \frac{1}{4} \times \frac{2}{3} \right) \times \left( x \times x^2 \right) \times \left( y \times y \right) \times z^2 \]

\[ = \left( \frac{1}{4} \times \frac{2}{3} \right) \times \left( x^{1 + 2} \right) \times \left( y^{1 + 1} \right) \times z^2 \]

\[ = \frac{1}{6} x^3 y^2 z^2\]

Thus, the answer is \[\frac{1}{6} x^3 y^2 z^2\].