I'm still learning this game and I think I finally understand all but two standard powers. I am still confused on energy explosion and pulse wave could anyone explain them to me?

what are you confused about with these two powers?

Pulse Wave
The acting character makes a ranged attack with their range value cut in half. All of the powers and abilities of the character "in the wave" (i.e., within range) are ignored. So if they are using Stealth and cannot normally be seen for a line of fire, they are still targeted. If they have Energy Shield/Defelection and would normally get a +2 to their defense against a ranged attack, it is ignored. The only thing that would block lines of fire is terrain. So you roll the dice and determine who you hit (Pulse Wave is unusual in that you might hit your own characters). Bear in mind that terrain effects the attack normally, so characters in/through hindering get +1 to their defense.

How much do you hit for? Well, that depends on how many characters are "in the wave" (not hit, potentially hit). If there is only one character in the wave, then you use your regular damage value (and since Pulse Wave ignores powers, if they have Toughness or something like that, it cannot be used). If there is two or more characters, then your damage value is 1 for the attack.

Energy Explosion
Target an opposing character. Make a ranged attack. All of this follows the normal ranged attack rules. Once you've determined that you hit someone, you ALSO check the defense values of the characters adjacent to the target (including friendly characters). Once you know who is hit, you deal each of these characters one damage.

Where Energy Explosion gets more complicated is when the attacking character has more than one . If the character has , then he can target 2 characters. Then, you check the characters adjacent to EACH hit character. To figure out damage, calculate the number of times hit due to being a target and add in the number of times hit due to being adjacent to a target and that gets you the total damage dealt to the character. For example:

. . . . A .
E . . . B D
. . . . C .

In the above diagram, let's say that E has and he targets A, B, and C. His roll is high enough to hit A and B, but not enough to hit C.

A - would be dealt 2 damage. Once for being hit, a second for being adjacent to B.
B - would normally be dealt 2 damage. Once for being hit, a second for being adjacent to A. However, B also has Toughness, so he reduces damage dealt to him by 1. So in the end, he only takes 1 damage.
C - he was missed both as a target and as someone adjacent to B. He is not dealt any damage.
D - he needs to be checked for being hit because he is adjacent to not one but two targets that were hit. When you see that the roll is high enough to hit him too, he is dealt 2 damage - one for being adjacent to A, another for being adjacent to B.

There are other interactions that are important for both Pulse Wave and Energy Explosion, but this is the general idea.

Ok thanks that made alot of sense to me explained that way. So it ignores stealth/damage absorbers/ect...... Does full damage if hits one and if it's multiple it hits each for 1.

Correct. Bear in mind that a critical hit will add 1 to either one of those situations.

Also, I updated the above for Energy Explosion.

Not quite...

The number HIT isn't the important thing. It's based on the number who could be hit.

If there are 4 guys in the PW radius and you only hit one of them you do not do full damage.