Rewrite the Expression as the Sum And/or Difference of Logarithms $$\log _ { 2 } \frac { \sqrt [ 5 ] { m } \sqrt [ 9 ] { n } } { k ^ { 2 } }$$

Multiple Choice

Rewrite the expression as the sum and/or difference of logarithms, without using exponents. Simplify if possible.
- $$\log _ { 2 } \frac { \sqrt [ 5 ] { m } \sqrt [ 9 ] { n } } { k ^ { 2 } }$$

A) $5 \log _ { 2 } m + 9 \log _ { 2 } n - 2 \log _ { 2 } k$
B) $\frac { 5 } { 2 } \log _ { 2 } \mathrm {~m} + \frac { 9 } { 2 } \log _ { 2 } \mathrm { n } - \frac { 1 } { 2 } \log _ { 2 } \mathrm { k }$
C) $\frac { 1 } { 5 } \log _ { 2 } \mathrm {~m} \cdot \frac { 1 } { 9 } \log _ { 2 } \mathrm { n } \div 2 \log _ { 2 } \mathrm { k }$
D) $\frac { 1 } { 5 } \log _ { 2 } \mathrm {~m} + \frac { 1 } { 9 } \log _ { 2 } \mathrm { n } - 2 \log _ { 2 } \mathrm { k }$