What does the raised $2$ stand for? My first guess was: $4^2$ is $2\times 4=8$?
Note: Am not really good at math
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It is called 'exponent' or 'power'.
Here $4^2$ means $4$ multiplied twice or in other words product of two $4's$. So: $$4^2 = 4*4 = 16$$ Similarly $7^3$ means $7$ multiplied thrice or in other words product of three $7's$. So: $$7^3 = 7*7*7 = 343$$ Since you are a starter, you can get more information about it here.