{(3root a raise to 4 ) raise to -3/2} raise to -1/2 solve and explain

The expression you provided is a bit complex, but let's break it down step by step:

1. First, let's simplify the innermost expression: (3√a)^4. This means that we are taking the cube root of 'a', then raising it to the power of 4.

2. Next, we take the result of that and raise it to the power of -3/2. The negative sign in the exponent means we take the reciprocal of the base. The 3/2 means we take the square root of the base and then cube it.

3. Finally, we take the result of that and raise it to the power of -1/2. Again, the negative sign in the exponent means we take the reciprocal of the base, and the 1/2 means we take the square root.

So, the expression simplifies as follows:

1. (3√a)^4 = a^(4/3)
2. (a^(4/3))^(-3/2) = a^(-2)
3. (a^(-2))^(-1/2) = a^1 = a

So, the simplified form of the given expression is 'a'.