First, let's simplify the numerator using these two rules for exponents:
a = a^color(red)(1) and (x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))
(ab)^-1/(cd^-2) = (a^color(red)(1)b^color(red)(1))^color(blue)(-1)/(cd^-2) = (a^(color(red)(1)xxcolor(blue)(-1))b^(color(red)(1)xxcolor(blue)(-1)))/(cd^-2) = (a^-1b^-1)/(cd^-2)
Now, we can deal with the terms with negative exponents using these rules for exponents:
x^color(red)(a) = 1/x^color(red)(-a) and 1/x^color(red)(a) = x^color(red)(-a)
(a^color(red)(-1)b^color(red)(-1))/(cd^color(red)(-2)) = d^color(red)(- -2)/(a^color(red)(- -1)b^color(red)(- -1)c) = d^color(red)(- -2)/(a^color(red)(- -1)b^color(red)(- -1)c) = d^color(red)(2)/(a^color(red)(1)b^color(red)(1)c)
Now, we can finalize the simplification by applying this rule for exponents:
a^color(red)(1) = a
d^color(red)(2)/(a^color(red)(1)b^color(red)(1)c) = d^2/(abc)