[ 9x^5y^-6 ] multiplied by [ 1 over 5(x^4 y^2)^-2 ] (dividing by x is the same as multiplying by 1/x)

Simplify the denominator (right hand terms). That part is the same as:

(x^4 y^2)^2 over 5 - when you take the negative of an exponent it moves it between the numerator and denominator. E.g. x^-2 is the same as 1/x^2; or x^2 is the same as 1/x^-2.

Now we multiply out the brackets. When we multiply together two terms x^n and x^m we add their exponents; when we raise one to another power like (x^n)^m, we multiply the exponents to get x^nm. Do that here to each exponent: