Why/how does the exponent of 1/2 mean the square root?

Answer 1

you know that

x^a * x^b = x^(a+b)

x^(1/2) * x^(1/2) = x^(1/2 + 1/2) = x^1 = x

√x * √x = x

(√x)^2 = (x^(1/2))^2 = x^(2 * 1/2) = x^1 = x