Say element \{11001010\}_2 and \{1101110\}_2 are both element of composite field GF(((2^2)^2)^2) which is generated using the following irreducible polynomials:

r(x) = x^2 + x + \{1000\}_2 between GF(2^8)/GF(2^4)
s(x) = x^2 + x + \{10\}_2 between GF(2^4)/GF(2^2)
t(x) = x^2 + x + 1 between GF(2^2)/GF(2)

how do I perform multiplication between \{11001010\}_2 and \{1101110\}_2?

also (1101110)^2?

thank you very much!