This tutorial explains how to make cool-looking explosions like these:
However, the user must have a basic knowledge of MAX and some of its functions, like creating combustion gizmos, the video post basic functions, omni lights, etc.
Now, without further rambling...
1. Create a SphereGizmo anywhere in the scene. Just place it somewhere in a place where it can easily be found, like as shown below.
2. Add a combustion to the SphereGizmo. The setting should be around:
Flame Type: Tendril
Flame Size: 20.0
The colors for the combustion are as follows:
Inner color:
R: 255
G: 248
B: 241
Hue: 37
Sat: 54
Value: 255
Outer color:
R: 255
G: 120
B: 30
Hue: 17
Sat: 225
Value: 225
Of course, there's nothing wrong with trying something different.
3. Make an omni light in the center of the combustion gizmo. Put some attentuation on it. This is the light that will *supposedly* light up the object you're....lighting up 
4. Color said omni light orange.
5. Create a particle SuperSpray with the following settings and place it inside the center of the SphereGizmo.
Basic Parameters:
Off Axis: 90.0
Spread: 90.0
Off Plane: 0.0
Spread: 180.0
Particle Generation:
Use Rate: 20
Speed: 5.0
Variation: 50.0
Particle Size: 3.0
Particle Type:
Tetra
Rotation and Collision:
Set to "Direction of Travel/MBlur", and set it to 15.
Next, select said SuperSpray, right-click on it, go to Properties, and assign it an Object ID. Assign it any # you want, but for this exercise it will be 32. Then, go to the Material Editor, and create something that's totally glowing white, either using self-illumination or raytrace luminosity. Apply that material to the particle spray.
The particle spray should look something like this, if you advance the frames enough:
6. Now for the hard part. Go to Rendering->Video Post. First of all (do this first), click on the blue thing:
After you click, select "Perspective" from the list of viewports and press OK. Then, you will need to put a lens flare in the middle of the explosion. Click on "Add Image Filter Event", and add a lensflare:
Setup the lensflare. You can either use a provided lens flare file made for explosions/quantum singularities/whatever, or you can use the AFTERFX3.lzf file pre-included with MAX, and red-shift the glows, red-and-orange-shift the manual secondries, increase first manual secondary size to at least twice that of the glow, and apply inferno (gaseous) to the manual secondaries.
Anyway you should have a lensflare looking something like this:
Then, when you have the lens flare right, go to "Node Sources" and pick the omni light as the node source. Press OK. Find a frame where the particles look good, and go to that frame in the video post renderer and render.
Then, back to the video post. Add a Lens Flare Glow. The settings for it are like:
Object ID: [whatever # you assigned the superspray]
Size: 0.2
Set glow color to "pixel", the color is something that will make it look better, like yellow, orange, blue, etc. If you really feel like it, you can use a gradient .
The video post thingy should look like this:
Remember, what you call the lensflare and the SuperSpray glow can be anything you want.
By the way, render the image:
