Question

Find each of the following product: 

\[\left( - \frac{7}{5}x y^2 z \right) \times \left( \frac{13}{3} x^2 y z^2 \right)\]

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:

\[\left( - \frac{7}{5}x y^2 z \right) \times \left( \frac{13}{3} x^2 y z^2 \right)\]

\[ = \left( - \frac{7}{5} \times \frac{13}{3} \right) \times \left( x \times x^2 \right) \times \left( y^2 \times y \right) \times \left( z \times z^2 \right)\]

\[ = \left( - \frac{7}{5} \times \frac{13}{3} \right) \times \left( x^{1 + 2} \right) \times \left( y^{2 + 1} \right) \times \left( z^{1 + 2} \right)\]

\[ = - \frac{91}{15} x^3 y^3 x^3\]

Thus, the answer is \[- \frac{91}{15} x^3 y^3 x^3\].