Question
Find following product:
$\big(-\frac{1}{27}\text{a}^2\text{b}^2\big)\times\big(\frac{9}{2}\text{a}^3\text{b}^2\text{c}^2\big)$
$\big(-\frac{1}{27}\text{a}^2\text{b}^2\big)\times\big(\frac{9}{2}\text{a}^3\text{b}^2\text{c}^2\big)$
✓
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:
$\big(-\frac{1}{27}\text{a}^2\text{b}^2\big)\times\big(\frac{9}{2}\text{a}^3\text{b}^2\text{c}^2\big)$
$=\big[\big(-\frac{1}{27}×\frac{9}{2}\big)\big]×\big(\text{a}^2×\text{a}^3\big)×\big(\text{b}^2×\text{b}^2\big)×\text{c}^2$
$=\big[\big(-\frac{1}{27}×\frac{9}{2}\big)\big]\times\big(\text{a}^{2+3}\big)\times\big(\text{b}^{2+2}\big)\times\text{c}^2$
Thus, the answer is $−\frac{1}{6}\text{a}^5\text{b}^4\text{c}^2.$
We have:
$\big(-\frac{1}{27}\text{a}^2\text{b}^2\big)\times\big(\frac{9}{2}\text{a}^3\text{b}^2\text{c}^2\big)$
$=\big[\big(-\frac{1}{27}×\frac{9}{2}\big)\big]×\big(\text{a}^2×\text{a}^3\big)×\big(\text{b}^2×\text{b}^2\big)×\text{c}^2$
$=\big[\big(-\frac{1}{27}×\frac{9}{2}\big)\big]\times\big(\text{a}^{2+3}\big)\times\big(\text{b}^{2+2}\big)\times\text{c}^2$
Thus, the answer is $−\frac{1}{6}\text{a}^5\text{b}^4\text{c}^2.$
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