Hi I wonder if its posible to make such gaps in some clever way?
Yes absolutely. Here's a very simple method.
Select, then Copy, and Paste in Place one of the objects which you want to use to cut out the other.
Then set the stroke to black, and make the stroke thicker.
Send it behind the object using Object > Arrange > Send backwards. And then group both these objects together.
Wherever you move the grouped objects, the thicker stroke will automatically hide what's below.
When I double click the grouped object above, and enter isolation mode, you can see how it's constructed. The thicker black stroke outline becomes visible.
Also here is a slightly more little more complex method. This is ideal if you want to do the same over another background image such as a wall. You can use the same outline to create a mask.
Note that both these solutions are non-destructive, so if you have to edit it or move positions, nothing has been physically cut from the underlying shape.
Adding some Gaussian blurred copies achieves the final neon-like result
This is a drawing, it can well be done without ever cutting anything out. Of course it's easier if one can make something circular and then remove the extras. In this case the gear can be circular at first. Then one makes copies of the tools, add to them a wide stroke, expands it to a strokeless path and uses it to split the underlying circle with pathfinder panel functions or with Path > Divide objects below. It still needs manual tinkering to remove all remnants, but the gaps have consistent widths.
The scissors split paths well. In your image the gaps are not equal, so they probably are made one by one manually without any exact measuements..
Yes, you can easily create this design on PowerPoint. What you have to do? Download all the icons from nounproject or freepik (these are some free tools).Ungroup the icon one by one then group. You can give the gap in the icons manually. These are a few steps for creating gaps in the icon: 1) Take the gear icon. 2) Take two rectangles and place them in cross- shaped way. 3) Now, select all two shape and icon. Go to Format section > Merge Shapes > Subtract.
In this way, you can easily create that design.