What happens when a variable with an exponent is put under a square root?

A square root is simply an exponent of (1/2).

So if you had x^3 and you put that under a square root, it would be,

(x^3)^(1/2) - “x cubed raised to the one-half power”.

Exponent rules tells us to multiply the two exponents if a power is raised to another power.

So in our example above,
We’d have the exponent “3” multiplied with the exponent from the square root “1/2”.
This gives us 3/2.

So you could rewrite the problem from (x^3)^(1/2)
as x^(3/2).

Simply put, take the power of the variable under the square root, multiply it by 1/2 and that is the new power of the variable. :)