Rules of indices

Simplify the following:
(-2 x)^(-2)

Multiply each exponent in -2 x by -2:
(1)/((-2)^2 x^2)

(-2)^2 = 4:
 1/(4 x^2)

Also remember

$(-2x)^{-2}\,=\,\frac{1}{(2x)^2}\,=\,\frac{1}{(2x)(2x)}\,=\,\frac{1}{2\cdot x\cdot 2\cdot x}\,=\,\frac{1}{2\cdot2\cdot x\cdot x}\,=\,\frac{1}{4x^2}$