To solve for 2 to the power of 3 over 2, we first need to break it down into manageable parts. The expression can be written as:
2^(3/2) = 2^(3)^(1/2).
Calculating 2 to the power of 3 gives us:
2^3 = 2 × 2 × 2 = 8.
Next, we take the square root of 8:
(2^3)^(1/2) = (8)^(1/2) = √8.
We can simplify √8 further:
√8 = √(4 × 2) = √4 × √2 = 2√2.
Thus, 2 to the power of 3 over 2 is equal to:
2√2.