Simplify the following. Express your answer with positive exponents

12m^-8

or you can write 12/m^8 it is the same

Step-by-step explanation:

Let's to the denominator first

(m^4 n^-2)^3 * (m^-4 n^2)^-2

since (a^b)^c = a^bc

we can rewrite the second factor as

(m^4 n^-2)^2  I have done this to simply remove the -4 and 2 exponents and make them 4 and -2 as in the first factor

at this point you have the same quantities between brackets () and you can multiply, considering that a^b * a^c = a^(b+c)

so the denominator becomes (m^4 n^-2)^5

at this point I would simply use the exponents

(12m^6 n^-5)^2 / (m^4 n^-2)^5 = (12m^12 n^-10) / (m^20 n^-10)

therefore, simplifying the similar factors

12m^-8