The expression (3a^2 b^4 c^2)^2 (2a^4 b^2 c^4)^3 equals na^r b^s c^t

It ask what n, the leading coefficient is and I think it is 72? and to find the exponents r s and t would you just multiply it but whatever number is on the outside? or do I need to find the derivative??

yes 72.

Derivative? Methinks you are lost. This is not calculus at all, well below that, Algebra II, the law of exponents.
http://mathworld.wolfram.com/ExponentLaws.html

Go over those laws. As a check on your work...
2*2+3*4=r

Now as a personal note, if you are having problems with these and you are in calculus, I would do some soul searching about your math preparedness. Something is just not right here. If you put Calculus in your subj title and you are in Alg II, you are pretending to be something you are not, which again indicates some serious personal issues.

To find the leading coefficient, you just need to simplify the given expression.

Let's expand the expression and simplify it:

(3a^2 b^4 c^2)^2 (2a^4 b^2 c^4)^3
= (9a^4 b^8 c^4) (8a^12 b^6 c^12)
= 72a^16 b^14 c^16

From the simplified expression, we can see that the leading coefficient is indeed 72.

To find the exponents r, s, and t, you can use the powers rule. In this case, since the exponents are multiplied, you add the exponents of the same variable. So:

r = 16 (total exponent of a)
s = 14 (total exponent of b)
t = 16 (total exponent of c)

Therefore, the expression can be written as 72a^16 b^14 c^16. You do not need to find the derivative to determine the exponents.