The exponent symbol when typing is ^. so I so rewrite this for you.
(15x^8 / 24y^5) / (4x^4 / 8y^2)
I assumed you meant 8y squared because you said 8 squared.
now when we divide by a fraction, we can actually multiply by it's reciprocal and get the same thing. The word reciprocal really just means flip it over. so:
(15x^8 / 24y^5) * (8y^2 / 4x^4)
let's reduce the coefficients ( the numbers in front of the x and y) to make it easier.
We have 15/24 which can be reduced to 5/8
and 8/4 which is 2/1
so:
(5x^8 / 8y^5) * (2y^2 / x^4)
multiply numerator and denominator
(10x^8y^2) / (8x^4y^5)
now reduce coeffient. 10/8 is 5/4
reduce x: x^8/x^4 is x^4
reduce y: y^2/y^5 is 1/y^3
now put together
5x^4 / 4y^3
so C
Answer:
I think it's C is true but make sure
The question is incomplete. The complete question is :
Let X be a random variable with probability mass function
P(X =1) =1/2, P(X=2)=1/3, P(X=5)=1/6
(a) Find a function g such that E[g(X)]=1/3 ln(2) + 1/6 ln(5). You answer should give at least the values g(k) for all possible values of k of X, but you can also specify g on a larger set if possible.
(b) Let t be some real number. Find a function g such that E[g(X)] =1/2 e^t + 2/3 e^(2t) + 5/6 e^(5t)
Solution :
Given :

a). We know :
![$E[g(x)] = \sum g(x)p(x)$](https://tex.z-dn.net/?f=%24E%5Bg%28x%29%5D%20%3D%20%5Csum%20g%28x%29p%28x%29%24)
So, 

Therefore comparing both the sides,


Also, 
b).
We known that ![$E[g(x)] = \sum g(x)p(x)$](https://tex.z-dn.net/?f=%24E%5Bg%28x%29%5D%20%3D%20%5Csum%20g%28x%29p%28x%29%24)
∴ 

Therefore on comparing, we get

∴ 