Assuming your f(x) = x^3 +6x^2 +x^(1/2) and g(x) = x^(1/2), you have
.. f(x)/g(x) = x^(5/2) +6x^(3/2) +1
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If an exponent has any arithmetic in it, parentheses are needed around it.
Expectation = Sum of (item * Probability)
Expectation in this case:
$0*0.70 + $20000*0.16 + $40000*0.07 + $60000*0.05 + $80000*0.01 + $100000*0.01 = $ 10800