Anthony P. answered • 02/04/13

Experienced tutor in earth sciences and basic math to trigonometry

If I had to guess, I'd say the 5's and 3's are exponents? Working under this assumption:**36m ^{5}n^{3}_________**

**12m**

^{3}A property of exponents is the following:

**a ^{m} ÷ a^{n} = a**

^{(m-n)}

Note that this is the inverse operation when multiplying like bases with exponents:

**a ^{m} x a^{n} = a^{(m+n)}**

This can be illustrated if we expand the factors with exponents in this way,

**m*m*m*m*m****_____________**

**m*m*m**

You can see that the three m's on the denominator can be cancelled with three on the numerator, leaving m^{2} on the numerator, proving that the property m^{(5-3) }= m^{2}.

You can treat the coefficients separately, so that the ratio 36/12 is reduced to 3. The n^{3} factor is just along for the ride since it cannot be simplified further.

So putting it all together we get:

**3m ^{2}n^{3}**

Anthony P.

02/04/13