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Algebraic Expressions and Identities — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSAlgebraic Expressions and Identities3 Marks
Question
Find following product:
$\big(−\frac{24}{25}\text{x}^3\text{z}\big)×\big(\frac{−15}{16}\text{xz}^2\text{y)}$
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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:
$\big(−\frac{24}{25}\text{x}^3\text{z}\big)×\big(\frac{−15}{16}\text{xz}^2\text{y)}$
$=\big(-\frac{24}{25}×\frac{-15}{16}\big)×\big(\text{x}^3×\text{x})×\big(\text{z}\times\text{z}^2\big)\times\text{y}$
$=\big(-\frac{24}{25}×-\frac{15}{16}\big)×\big(\text{x}^{3+1}\big)×\big(\text{z}^{1+2}\big)\times\text{y}$
$=\frac{9}{10}\text{x}^4\text{y}\text{z}^3$
Thus, the answer is $=\frac{9}{10}\text{x}^4\text{y}\text{z}^3$

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