What have you tried so far? Where is your problem with these questions? Are wanting someone to just do the problems for you?
If you just need to see some examples, look here: Negative exponents - A complete course in algebra or one of the many other web sites having these kinds of problems. Or ask your teacher.
If you have a problem figuring out the answers, please show what you have tried and be more specific about where your problem is.
Well..... that sounds right.
Problem #1:
flip the fractions since the exponents are negative:
$\displaystyle \left(\frac{c^2}{a^{-3} b}\right)^4 \frac{a^4 b^{-3}}{c^5}$
"do" the exponents and multiply them:
$\displaystyle \frac{c^8}{a^{-12}b^4} \frac{a^4 b^{-3}}{c^5}$
subtract the exponents on the bottom from the top:
$\displaystyle a^{4--12} b^{-3-1} c^{8-5}$
$\displaystyle a^{16} b^{-4} c^3$
since the exponent on $\displaystyle b$ is negative, flip it back down into the denominator:
$\displaystyle \frac{a^{16} c^3}{b^4}$
Problem #2:
$\displaystyle \frac{\left(2a^{-1}b^4c^{-3}\right)^{-2}}{\left(4a^2bc^{-4}\right)^2}$
When working with the numbers, think of them in the most factored form you can. This means the $\displaystyle 4$ in the denominator should be thought of as $\displaystyle 2^2$. Looking at it this way, you will be able to easily combine it with the $\displaystyle 2$ in the numerator.
$\displaystyle \frac{2^{-2}a^2b^{-8}c^6}{2^4a^4b^2c^{-8}}$
Note that the $\displaystyle 2^2$ in the denominator was squared, so the exponents got multiplied.
$\displaystyle 2^{-6} a^{-2} b^{-10} c^{14}$
$\displaystyle \frac{c^{14}}{2^6 a^2 b^{10}}$
I left the $\displaystyle 2^6$ in exponential form. Depending on the instructions, you may want to call it $\displaystyle 64$ instead.
Let me know if you need more help with these.