# Find Each of the Following Product: ( 4 3 U 2 V W ) × ( − 5 U V W 2 ) × ( 1 3 V 2 W U ) - Mathematics

Find each of the following product: $\left( \frac{4}{3} u^2 vw \right) \times \left( - 5uv w^2 \right) \times \left( \frac{1}{3} v^2 wu \right)$

#### Solution

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:

$\left( \frac{4}{3} u^2 vw \right) \times \left( - 5uv w^2 \right) \times \left( \frac{1}{3} v^2 wu \right)$

$= \left\{ \frac{4}{3} \times \left( - 5 \right) \times \frac{1}{3} \right\} \times \left( u^2 \times u \times u \right) \times \left( v \times v \times v^2 \right) \times \left( w \times w^2 \times w \right)$

$= \left\{ \frac{4}{3} \times \left( - 5 \right) \times \frac{1}{3} \right\} \times \left( u^{2 + 1 + 1} \right) \times \left( v^{1 + 1 + 2} \right) \times \left( w^{1 + 2 + 1} \right)$

$= - \frac{20}{9} u^4 v^4 w^4$

Thus, the answer is $- \frac{20}{9} u^4 v^4 w^4$.

Concept: Multiplication of Algebraic Expressions
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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 6 Algebraic Expressions and Identities
Exercise 6.3 | Q 14 | Page 14