36m5n5 ÷ (12m3)

## 36m5n5 ÷ (12m3)

# 3 Answers

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}**

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

(36m^{5}n^{5})/(12m^{3})

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 x^{n}/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,

(36m^{5}n^{5})/(12m^{3})

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

(3m^{5}n^{5})/(m^{3})

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:

3m^{2}n^{5}

# Comments

My browser isn't playing nice with the edit button right now, so I just wanted to add that in the general case that I put - the m and n are separate from the problem and don't relate to our variables. Accidentally chose the exact same variables that we were working with!

36(m^{5})(n^{5})/ 12(m^{3})

= [36/12]*[m^{5-3}]*(n^{5})

= (3)*(m^{2})*(n^{5})

= 3m^{2}n^{5}

## Comments

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