Question

Find each of the following product: \[( - 7xy) \times \left( \frac{1}{4} x^2 yz \right)\]

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: 

\[\left( - 7xy \right) \times \left( \frac{1}{4} x^2 yz \right)\]

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

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

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

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