I've typed up in Word (it's easier for me to make equations in there) and uploaded as an image below a problem I came across, and I'm curious as to why this works. Obviously, since x,y,z are all positive numbers, if the numbers plugged in are all greater than 1, then it's simple. But x,y, and/or z can also be decimals. I'm curious to know why it works with these decimals as well, when raising to a higher power makes the value smaller.
If anyone can help me write up the proof, I would greatly appreciate it. Thanks in advance.