Find product: (0.5x)× (1 3 xy^2z^4)× (24x^2yz ) - Vidyadip

Question

Find product:
$(0.5\text{x})×\big(\frac{1}{3}\text{xy}^2\text{z}^4)×\big(24\text{x}^2\text{yz}\big)$

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Answer

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, $a^m \times a^n=a^{m+n}$.
We have:
$(0.5\text{x})×\big(\frac{1}{3}\text{xy}^2\text{z}^4)×\big(24\text{x}^2\text{yz}\big)$
$=\big(0.5×\frac{1}{3}×24)×\big(\text{x}×\text{x}×\text{x}^2)\\×\big(\text{y}^2×\text{y}\big)×\big(\text{z}^4×\text{z}\big)$
$=\big(0.5×\frac{1}{3}×24)×\big(\text{x}^{1+1+2}\big)\\×\big(\text{y}^{2+1}\big)×\big(\text{z}^{4+1}\big)$
$=4\text{x}^4\text{y}^3\text{z}^5$
Thus, the answer is $=4\text{x}^4\text{y}^3\text{z}^5$

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