Firstly, the rule with raising a power by a power is to multiply the two powers. In our case, it'll look like this:
[tex] (-2x^6y^{-2})^3\\ (-2)^3x^{6*3}y^{-2*3}\\ -8x^{18}y^{-6} [/tex]
Now the rule from negative exponents to fractions is [tex] x^{-m}=\frac{1}{x^m} [/tex] . Applying this to y^-6, your final answer is going to be [tex] \frac{-8x^{18}}{y^{6}} [/tex]
