Which of the following functions is reduced what will be the exponent on the M 27mn^3/51m^6n

When you divide a base with an exponent by a base with an exponent, you subtract the exponents together. (But you can only combine exponents when the bases are the same)

For example:

   (You can't combine them as they have different bases of x and y)

When you have a negative exponent, you move the base with the negative exponent to the other side of the fraction to make the exponent positive.

For example:

or

or    

     You can simplify the whole fraction or just "m" since you need to find the exponent of "m". I will simplify the whole fraction.

     Make all the exponents positive

   So the exponent of m = 5, your answer is the 3rd option

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this