Question
Find following product:
$\frac{1}{4}\text{xy}×\frac{2}{3}\text{x}^2\text{yz}^2$
$\frac{1}{4}\text{xy}×\frac{2}{3}\text{x}^2\text{yz}^2$
✓
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:
$\frac{1}{4}\text{xy}×\frac{2}{3}\text{x}^2\text{yz}^2$
$=\big(\frac{1}{4}×\frac{2}{3}\big)×\big(\text{x}×\text{x}^2)×(\text{y}×\text{y})×\text{z}^2$
$=\big(\frac{1}{4}×\frac{2}{3}\big)×\big(\text{x}^{1+2}\big)×\big(\text{y}^{1+1}\big)×\text{z}^2$
$=\frac{1}{6}\text{x}^3\text{y}^2\text{z}^2$
Thus, the answer is $=\frac{1}{6}\text{x}^3\text{y}^2\text{z}^2$
We have:
$\frac{1}{4}\text{xy}×\frac{2}{3}\text{x}^2\text{yz}^2$
$=\big(\frac{1}{4}×\frac{2}{3}\big)×\big(\text{x}×\text{x}^2)×(\text{y}×\text{y})×\text{z}^2$
$=\big(\frac{1}{4}×\frac{2}{3}\big)×\big(\text{x}^{1+2}\big)×\big(\text{y}^{1+1}\big)×\text{z}^2$
$=\frac{1}{6}\text{x}^3\text{y}^2\text{z}^2$
Thus, the answer is $=\frac{1}{6}\text{x}^3\text{y}^2\text{z}^2$
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