Solution:

Given: a = 3√2

To find: the value of a^(1/2) and a^(-1/2)

Simplifying the given expression:
We can write 3√2 as 3 * (2^(1/2))^(1/3)
Using the property of exponents, we can multiply the exponents:
= 3 * 2^((1/2) * (1/3))
= 3 * 2^(1/6)

Therefore, a = 3 * 2^(1/6)

Now, let's find the value of a^(1/2):

a^(1/2) = (3 * 2^(1/6))^(1/2)

Using the property of exponents, we can multiply the exponents:
= 3^(1/2) * (2^(1/6))^(1/2)
= √3 * (2^(1/6 * 1/2))
= √3 * 2^(1/12)

Therefore, the value of a^(1/2) is √3 * 2^(1/12).

Next, let's find the value of a^(-1/2):

a^(-1/2) = 1 / (3 * 2^(1/6))^(1/2)

Using the property of exponents, we can multiply the exponents:
= 1 / (3^(1/2) * (2^(1/6))^(1/2))
= 1 / (√3 * (2^(1/6 * 1/2)))
= 1 / (√3 * 2^(1/12))

Therefore, the value of a^(-1/2) is 1 / (√3 * 2^(1/12)).

In summary:

a^(1/2) = √3 * 2^(1/12)
a^(-1/2) = 1 / (√3 * 2^(1/12))

Therefore, the value of a^(1/2) is √3 * 2^(1/12) and the value of a^(-1/2) is 1 / (√3 * 2^(1/12)).