Exercise:
Compare the following values:
2^(2^3) and 3^(3^2)
Solution:
First, we can simplify the exponents in the parentheses for each expression:
2^(2^3) = 2^8 = 256
3^(3^2) = 3^9 = 19683
Therefore, 2^(2^3) is smaller than 3^(3^2).
This is apparent by knowing that 3^2 = 9 is much greater than 2^3 = 8, which means 3^(3^2) will be a much larger value compared to 2^(2^3), making 3^(3^2) the larger value.
So, the answer is 3^(3^2) > 2^(2^3).