Question

Find each of the following product: \[\left( \frac{- 24}{25} x^3 z \right) \times \left( - \frac{15}{16}x z^2 y \right)\]

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:

\[\left( - \frac{24}{25} x^3 z \right) \times \left( - \frac{15}{16}x z^2 y \right)\]

\[ = \left\{ \left( - \frac{24}{25} \right) \times \left( - \frac{15}{16} \right) \right\} \times \left( x^3 \times x \right) \times \left( z \times z^2 \right) \times y\]

\[ = \left\{ \left( - \frac{24}{25} \right) \times \left( - \frac{15}{16} \right) \right\} \times \left( x^{3 + 1} \right) \times \left( z^{1 + 2} \right) \times y\]

\[= \frac{9}{10} x^4 y z^3\]

Thus, the answer is \[\frac{9}{10} x^4 y z^3\].