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Algebraic Expressions and Identities — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsAlgebraic Expressions and Identities2 Marks
Question
Find product:
$\big(\frac{7}{9}\text{ab}^2\big)×\big(\frac{15}{7}\text{ac}^2\text{b}\big)×\big(\frac{−3}{5}\text{a}^2\text{c})$
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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:
$\big(\frac{7}{9}\text{ab}^2\big)×\big(\frac{15}{7}\text{ac}^2\text{b}\big)×\big(\frac{−3}{5}\text{a}^2\text{c})$
$=\big[\big(\frac{7}{9}\big)×\big(\frac{15}{7}\big)×\big(−\frac{3}{5}\big)\big]×(\text{a}×\text{a}×\text{a}^2)\\×(\text{b}^2×\text{b})×(\text{c}^2×\text{c})$
$=\big[\big(\frac{7}{9}\big)×\big(\frac{15}{7}\big)×\big(−\frac{3}{5}\big)\big]×\big(\text{a}^{1+1+2}\big)\\×\big(\text{b}^{2+1}\big)×\big(\text{c}^{2+1}\big)$
$=−\text{a}^4\text{b}^3\text{c}^3$
Thus, the answer is $=−\text{a}^4\text{b}^3\text{c}^3$

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