Simplify the expression x^-4×y^3×x^4×y^2.

For simplifying an expression like this where the same bases with different exponents are to be multiplied, remember the Product rule. It says that when multiplying two or more powers having the same base (x and y in this case), you must add the exponents. For example, here in this expression there are two x's and two y's with different powers so you can simple add the powers of x and for y like shown below:

x^-4×y^3×x^4×y^2

= x^(-4+4) × y^(3+2)

=x^1 × y^5

since x^1 = x so we can omit the power 1 and write x instead.

xy^5 (here the power 5 only raises y and not x since it is not applied to whole)

yes. we do proportions in probabilities.