HELPPPPPPPPPPPP and explain

Start by eliminating anything with a z in it. z to the zero power is 1. That means that the top one and the third one from the bottom is gone.

If you want to remove the power (3/4) the rule is that you multiply every power inside the brackets by 3/4.
2 has a power of 1 
2^1 is the way you think of it.
(2^1)^3/4 = 2^(3/4). It would look like this.[tex]2^\frac{3}{4} [/tex]


(a ^2 ) ^(3/4) = 2^(6/4) which would look like this [tex]a^\frac{6}{4} [/tex]
which could be written as [tex]a^\frac{3}{2} [/tex] or a^1.5

x ^ (-5) can be written as [tex]x^\frac{-15}{4} [/tex] Notice that - 5 * 3/4 = - 15/4 It could also be written as 1/x^(15/4) That would get rid of the - sign. 

(y ^ 8) ^(3/4) = y^(24/4) = y^6

On your page, number the questions from a to h

e is the only one I found to be correct.  I will go through the errors. Sometimes I did not list them all. There's just too many of them. The key point is that all the powers are multiplied by 1/4. You need 4 letters or numbers to take 1 letter or number outside the root sign.

a
wrong because a should be 6/4 and not 5/4. As noted, this may not be the only error.

b 
is because the y should be y^1 outside the root sign and y^2 inside the root. 

c
is wrong because there should be a y^2 inside the brackets.

d
is wrong 2 should be 8 raised the the 1/4 power. 8^1/4

e
correct but I sure don't like z^0 sitting there.

f
has all kinds of problems. Start with the 268 That is wrong. If you are going to bring 36 inside the root sign, it should be 36^3 which is 44656. y is wrong and so is x. For x you will have to use the -15 somewhere.

g
is wrong. The 36 is not to be altered and if it is it must be done as it was in the above question
y should be to the 6/4

h 
is wrong. You lost a y somewhere.

Remark
Up until now, the questions you have asked could have been answered and it would have cleared up any of the problems you have been having. This one is quite different. 

It is extremely long and it supposes that you know the multiplication rule for powers. You must have been been taught something before you tackled this monster. You need to go to a help center if you are in school or ask a tutor if you are not. It is not you that's the problem. It's the question that's the problem. It is very long and there are all sorts of tricks in it. In my opinion, it's not really a fair question without a lot of help.