Question

(m/n)^-x:(m/2n)^-x =

Answer 1

Maybe it helps to write it as fractions:\[\frac{ \left(\frac{ m }{ n } \right)^{-x} }{ \left(\frac{ m }{ 2n } \right)^{-x} }\]Now we can write it as one power:\[\left( \frac{ \frac{ m }{ n } }{ \frac{ m }{ 2n } }\right)^{-x}\]Which is the same as:\[\left( \frac{ m }{ n }\frac{ 2n }{ m } \right)^{-x}\]All the n's and m's cancel out:\[2^{-x}\]This could be rewritten as\[\frac{ 1 }{ 2^x }=\left( \frac{ 1 }{ 2 } \right)^x\]Take your pick!