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Algebraic Expressions and Identities — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSAlgebraic Expressions and Identities3 Marks
Question
Find product: $\Big(\frac{−2}{7}\text{a}^4\Big)×\Big(\frac{−3}{4}\text{a}^2\text{b}\Big)×\Big(\frac{−14}{5}\text{b}^2\Big)$
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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:
$\Big(\frac{−2}{7}\text{a}^4\Big)×\Big(\frac{−3}{4}\text{a}^2\text{b}\Big)×\Big(\frac{−14}{5}\text{b}^2\Big)$
$=\Big[\big(\frac{−2}{7}\big)×\big(\frac{−3}{4}\big)×\big(\frac{−14}{5}\big)\Big]×(\text{a}^4×\text{a}^2)×(\text{b}×\text{b}^2)​​​​​​​$
$=−\Big(\frac{2}{7}×\frac{3}{4}×\frac{14}{5}\Big)×\text{a}^{4+2}×\text{b}^{1+2}$
$=−\frac{3}{5}\text{a}^6\text{b}^3$
Thus, the answer is $=−\frac{3}{5}\text{a}^6\text{b}^3$

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