Perform the indicated operation and write your answer with positive integer exponents.
-$$\frac { ( \mathrm { mn } ) ^ { - 1 } } { \mathrm {~m} ^ { - 2 } + \mathrm { n } ^ { - 2 } }$$
A) $\frac { m n } { n + m }$
B) $\frac { n } { n ^ { 2 } - m ^ { 2 } }$
C) $\frac { m ^ { 2 } + n ^ { 2 } } { m n }$
D) $\frac { m n } { n ^ { 2 } + m ^ { 2 } }$

Question

Quizplus · Accepted Answer

The expression simplifies to $\frac{1}{m^{-2} + n^{-2}}$ which is $\frac{1}{\frac{1}{m^2} + \frac{1}{n^2}}$. Simplifying further, it becomes $\frac{m^2n^2}{n^2 + m^2}$, which simplifies to $\frac{mn}{n^2 + m^2}$.

Perform the Indicated Operation and Write Your Answer with Positive (mn)−1 m−2+n−2\frac { ( \mathrm { mn } ) ^ { - 1 } } { \mathrm {~m} ^ { - 2 } + \mathrm { n } ^ { - 2 } } m−2+n−2(mn)−1​

Perform the Indicated Operation and Write Your Answer with Positive $\frac { ( \mathrm { mn } ) ^ { - 1 } } { \mathrm {~m} ^ { - 2 } + \mathrm { n } ^ { - 2 } }$