Question

How do you divide \[\dfrac{{{m^3}{n^2}}}{{{m^{ - 1}}{n^3}}}\] ?

Answer 1

Hint: In this question, the powers of each variable present in the denominator need to be subtracted from that in the numerator to gain the final expression for representing a variable. Also, properties of exponents are to be applied here.

Complete step by step solution:
We have the fraction as \[\dfrac{{{m^3}{n^2}}}{{{m^{ - 1}}{n^3}}}\] . In the question, division needs to be performed.
For this, we first need to analyse the fraction. We have \[{m^3}{n^2}\] as the numerator, and \[{m^{ - 1}}{n^3}\] as the denominator. It is clear that we need to perform division after simplifying the fraction further.
Now, \[{m^{ - 1}}\] can also be written as \[\dfrac{1}{m}\] . Then, we will obtain the expression as \[\dfrac{{\dfrac{{{m^3}{n^2}}}{{{m^{ - 1}}{n^3}}}}}{m}\] .
On simplifying this, we will get \[\dfrac{{{m^4}{n^2}}}{{{n^3}}}\] .
Now, to obtain the final answer, we need to solve this fraction, i.e., we need to divide \[{m^4}{n^2}\] by \[{n^3}\] .
Since the power of \[n\] in the denominator is greater than that in the numerator, there will be a term remaining in the denominator. Hence, the fraction we obtain will be \[\dfrac{{{m^4}}}{n}\] .
This is the final answer, i.e., on dividing \[\dfrac{{{m^3}{n^2}}}{{{m^{ - 1}}{n^3}}}\] , we will get the answer as \[\dfrac{{{m^4}}}{n}\] .
So, the correct answer is “ \[\dfrac{{{m^4}}}{n}\]”.

Note: A simple fraction (also known as a common fraction) is a rational number written as \[\dfrac{a}{b}\] or \[a/b\] ​, where \[a\] and \[b\] are both integers. As with other fractions, the denominator \[b\] cannot be zero. Fractions are used widely in real life situations, when we need to express something as a part of a bigger thing.
If the same variable is present in both numerator and the denominator, then the powers of the denominator term can be subtracted from that of the numerator term to obtain a simplified expression.