Question

How do you simplify the given product ${{m}^{4}}\left( {{m}^{2}} \right)$?

Answer 1

We start solving the problem by equating the given product to a variable. We then recall the law of exponents that ${{a}^{m}}\times {{a}^{n}}={{a}^{m+n}}$. We then make use of this law of exponents to proceed through the problem. We then make the necessary calculations involving addition operations to get the required answer for the given product in the problem.

Complete step by step answer:
According to the problem, we are asked to simplify the given product: ${{m}^{4}}\left( {{m}^{2}} \right)$.
Let us assume $d={{m}^{4}}\left( {{m}^{2}} \right)$ ---(1).
We can see that the R.H.S (Right Hand Side) of the equation (1) resembles the form ${{a}^{m}}\times {{a}^{n}}$. From the law of exponents, we know that ${{a}^{m}}\times {{a}^{n}}={{a}^{m+n}}$. So, let us use this result in equation (1).
Now, we get $d={{m}^{4+2}}$.
$\Rightarrow d={{m}^{6}}$.
So, we have found the simplified form of the given product ${{m}^{4}}\left( {{m}^{2}} \right)$ as ${{m}^{6}}$.
$\therefore$ The simplified form of the given product ${{m}^{4}}\left( {{m}^{2}} \right)$ is ${{m}^{6}}$.

Note:
Whenever we get this type of problem, we first check whether we can use any laws of exponents which will help us to get an answer. We can also simplify the given product by performing trial and error method by assuming values for the variable m and then simplifying to the required form. We should not make calculation mistakes after applying the law of exponents as it will provide wrong answers to the given problem. Similarly, we can expect problems to find the simplified form of $\dfrac{{{\left( {{m}^{2}} \right)}^{3}}}{{{m}^{8}}}$.