Question

How do you simplify $ {r^3}.{r^{ - 2}} $ ?

Answer 1

Hint: The above simplification can be only done by using some laws or results. Since the question involves things such as the same base and different power it gets eventually cleared that laws of indices are to be used. There are a total six laws of indices out of one is applicable over here.

Complete step-by-step answer:
Looking at the question you should realize that the law of indices should be used.
We use this law of indices mostly to simplify expressions when the bases are the same with different powers as given in the above question.
There are a total six laws of indices .
We are going to use the following one:
The law states that $ {x^m}.{x^n} = {x^{m + n}} $
now comparing the above question we can relate it to the law
hence we will obtain the following solution
 $
  {r^3}.{r^{ - 2}} = {r^{3 + \left( { - 2} \right)}} \\
   \Rightarrow {r^3}.{r^{ - 2}} = {r^{3 - 2}} \\
   \Rightarrow {r^3}.{r^{ - 2}} = {r^{3 - 2}} \;
 $
Hence the value of $ {r^3}.{r^{ - 2}} $ will be $ r $ respectively.
So, the correct answer is “r”.

Note: The level of difficulty of the above question is very little when compared to the use of laws of indices. Laws of indices are used broadly in various fields other than maths. These are also referred to as exponents. This law makes it easier to solve the equations which are already in compressed form.