Why is (5+2) to the second power is not equal to 5 to the second power plus 2 to the second power is not equal

Because 5 +2 is 7 and seven to the second power is 49. On the other hand 5 squared is 25 and 2 to the second power is 4 when you ad them together you get 29 you are taking to completely different numbers to the power of two and that’s why they aren’t equal

This answer is a lot easier to find if you write out the math. 5 to the second power (or 5X5) is 25 and 2 to the second power (or 2X2) is 4, so they add together for a sum of 29 (25+4=29). As for (5+2) to the second power, both five and two are taken to the second power, however when you distribute there are middle terms that result as well. A good way to approach it is to use the foil method, which stands for First, Outter, Inner, Last.
So (5+2) to the second power can also be written:
(5+2)(5+2)
First: 5X5 =25
Outter: 5X2 =10
Inner: 2X5 = 10
Last: 2X2 =4
And all of that adds up for a total of 49.