Question

Find the product of the following monomial: kl, lm, km, klm. And choose from the options given below.
(a). \[{{k}^{3}}{{l}^{3}}{{m}^{3}}\]
(b). \[{{k}^{4}}{{l}^{3}}{{m}^{3}}\]
(c). \[{{k}^{3}}{{l}^{4}}{{m}^{3}}\]
 (d). None of these.

Answer 1

Hint: To solve this question, we will first of all consider all the given monomials given as kl, lm, km, klm and will multiply them separately one at a time to get the desired result.

Complete step-by-step solution -

The monomials are given as kl, lm, km, klm.
We need to calculate the product of the given monomials.
 First of all, we will multiply kl with lm, we have,
\[(kl)(lm)=k{{l}^{2}}m\] .
 Now we will multiply the obtained number by km which gives,
\[(k{{l}^{2}}m)(km)={{k}^{2}}{{l}^{2}}{{m}^{2}}\] .

Now lastly multiplying the obtained number by klm we get,
\[({{k}^{2}}{{l}^{2}}{{m}^{2}})(klm)={{k}^{3}}{{l}^{3}}{{m}^{3}}\].
Therefore, we got the answer to the desired question as the product of three given monomials is \[{{k}^{3}}{{l}^{3}}{{m}^{3}}\].
Matching from the options given in the question we have, option (a) is the correct answer to the given question.

Note: The possibility of error in this question can be directly multiplying all the given monomials at once and not separately one at a time. This could lead to multiplication errors and hence you could arrive at an incorrect solution. So better is to opt for one monomial multiplication at a time to avoid errors.