Question

Find each of the following product:

\[\left( 0 . 5x \right) \times \left( \frac{1}{3}x y^2 z^4 \right) \times \left( 24 x^2 yz \right)\]

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:

\[\left( 0 . 5x \right) \times \left( \frac{1}{3}x y^2 z^4 \right) \times \left( 24 x^2 yz \right)\]

\[ = \left( 0 . 5 \times \frac{1}{3} \times 24 \right) \times \left( x \times x \times x^2 \right) \times \left( y^2 \times y \right) \times \left( z^4 \times z \right)\]

\[ = \left( 0 . 5 \times \frac{1}{3} \times 24 \right) \times \left( x^{1 + 1 + 2} \right) \times \left( y^{2 + 1} \right) \times \left( z^{4 + 1} \right)\]

\[ = 4 x^4 y^3 z^5\]

Thus, the answer is \[4 x^4 y^3 z^5\].