Question

How do you multiply $\dfrac{{{u^2}{v^4}}}{{u{v^3}}} \cdot \dfrac{{uv}}{v} \cdot \dfrac{{{u^3}{v^3}}}{{{u^2}v}}$?

Answer 1

Hint: The question deals with the multiplication of algebraic expression. An algebraic expression is a set of operations which should be done by a specific set of orders. When an algebraic expression requires mathematical operation of multiplication, then the process of multiplication is called the multiplication of algebraic expression. When different expressions give the same answer they are called equivalent expressions. An algebraic expression can have many types of algebraic terms. Exponent in the mathematical expression is the number that signifies the number of times the quantity has been multiplied by itself.in multiplication the product of two factor with same signs will be positive and the product of two number with unlike signs will be negative.in multiplication the power of same variables get added. When the two algebraic terms having minus signs multiplied together, then the result will be positive.

Complete step by step answer:
Step: 1 the given algebraic expression is,
$\dfrac{{{u^2}{v^4}}}{{u{v^3}}} \cdot \dfrac{{uv}}{v} \cdot \dfrac{{{u^3}{v^3}}}{{{u^2}v}}$
Cancel the same term from numerator and denominator of the expression.
Therefore
$ \Rightarrow \dfrac{{{u^2}{v^4}}}{{u{v^3}}} \cdot \dfrac{{uv}}{v} \cdot \dfrac{{{u^3}{v^3}}}{{{u^2}v}} = \dfrac{{{u^3}}}{{{v^3}}}$

Therefore given expression is multiplied and the outcome is $\dfrac{{{u^3}}}{{{v^3}}}$

Note: While multiplying the algebraic expression we often forget to multiply the signs of the term in the expression. Always check the term having the same sign and multiply them first to avoid any mistake. Find the exponential term having the same power in both, numerator and denominator and cancel them from each other. Multiply the same term in numerator as well as in denominator with their signs. Common mistakes students do in multiplication of negative terms. Always keep note that one negative and one positive will result negative.