Question
Find product: $\big(\frac{2}{5}\text{a}^2\text{b}\big)×(−15\text{b}^2\text{ac}\big)×\big(\frac{−1}{2}\text{c}^2\big)$

Answer

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:
$\big(\frac{2}{5}\text{a}^2\text{b}\big)×(−15\text{b}^2\text{ac}\big)×\big(\frac{−1}{2}\text{c}^2\big)$
$=\big[-\frac{2}{5}×(−15)×(−\frac{1}{2})\big]×\big(\text{a}^2×\text{a})\\×\big(\text{b}×\text{b}^2\big)×\big(\text{c}×\text{c}^2)​​​​​​​$
$=\big[-\frac{2}{5}×(−15)×(−\frac{1}{2})\big]×\big(\text{a}^{2+1}\big)\\×\big(\text{b}^{1+2}\big)×\big(\text{c}^{1+2}\big)$
$=3\text{a}^3\text{b}^3\text{c}^3$
$\because$ The expression doesn't consist of the variables x and $y.$
$\therefore$ The result cannot be verified for $x = 1$ and $y = 2$
Thus, the answer is $3\text{a}^3\text{b}^3\text{c}^3$

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