For this case we have that by definition of power properties it is fulfilled that:
[tex]a ^ {-1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]
Then, if we have the following expression:
[tex](2x)^{ -1}[/tex]
Applying the property, we can rewrite the expression as:
[tex]\frac {1} {(2x) ^ 1} = \frac {1} {2x}[/tex]
Answer:
[tex]\frac {1} {2x}[/tex]
