C
[tex] { x}^{ - y} = \frac{1}{ {x}^{y} } \\ \frac{1}{ {x}^{ - y} } = {x}^{y} [/tex]
so, start by converting all variables with negative exponents so that they now have positive exponents:
[tex] \frac{ - 16 {a}^{ - 3} {b}^{ - 5} }{2 {a}^{ - 4} {b}^{2} } = \frac{ - 16 {a}^{4} }{2 {a}^{3} {b}^{7} } [/tex]
Now, simplify by division:
[tex] \frac{ {x}^{y} }{ {x}^{z} } = {x}^{y - z} [/tex]
[tex] \frac{ - 16 {a}^{4} }{2 {a}^{3} {b}^{7} } = \frac{ - 8a}{ {b}^{7} } [/tex]
The answer is C
