c^8d^-12
________
c^-4d^-8
c^8d^-12 / c^-4d^-8
=c^(8-(-4)) d^(-12 - (-8))
=c^12 d^-4
= c^12/d^4
To simplify the expression, we can apply the laws of exponents.
The laws of exponents state that when dividing two numbers with the same base, you subtract the exponents.
In this case, we have c^8 divided by c^-4, and d^-12 divided by d^-8.
For the c terms, we subtract the exponents: 8 - (-4) = 8 + 4 = 12.
For the d terms, we subtract the exponents: -12 - (-8) = -12 + 8 = -4.
So the simplified expression becomes c^12d^-4.