36m5n5 ÷ (12m3)

Question

36m5n5 ÷ (12m3)

Answer 1

If I had to guess, I'd say the 5's and 3's are exponents? Working under this assumption:

36m⁵n³
_________
12m³

A property of exponents is the following:

a^m ÷ aⁿ = a^(m-n) 

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

a^m x aⁿ = 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 m² on the numerator, proving that the property m^(5-3) = m². 

You can treat the coefficients separately, so that the ratio 36/12 is reduced to 3. The n³ factor is just along for the ride since it cannot be simplified further. 

So putting it all together we get: 

3m²n³

Answer 2

I'm assuming that you're meaning to write the following:

(36m⁵n⁵)/(12m³)

In this case, we compare similar bases' exponents. We subtract the lesser from the higher number and keep the rest wherever the higher number is.

More generally, if we have xⁿ/x^m, it would simplify to x^n-m. You can see that in the case where m>n (n-m would be negative), then x^n-m would be written as 1/(x^m-n), if we want to keep positive exponents.

ANYWAY, in our case,

(36m⁵n⁵)/(12m³)

Let's first notice that 36/12 is equal to 3 = 3/1.

(3m⁵n⁵)/(m³)

Now, using our exponent rule from above, we can see that we have an m and n in the numerator, and m in the denominator. Since m is the only one in common, that's the only one we need to worry about simplifying. The 5 on top is bigger than 3 on the bottom, so we know that m is going to end up on top. 5-3=2, so we have 2 m's left over on top.

Our answer would be:

3m²n⁵

Answer 3

36(m⁵)(n⁵)/ 12(m³)

= [36/12]*[m^5-3]*(n⁵)

= (3)*(m²)*(n⁵)

= 3m²n⁵