We start solving the expression by using the laws of exponents. Specifically, we'll use the quotient rule, which states that a^(m) / a^(n) = a^(m-n). Let's apply that to our expression:
((a^(4)b^(2))/(a^(-8)b^(-6)))
This transforms into
a^(4 - (-8))b^(2 - (-6))
By removing the double negatives, we get
a^(12)b^(8)
We have this new expression raised to the power of (1/2). Now, we can utilize the power of a power rule, which says that (a^(m))^n = a^(m*n).
a^(12 * (1/2))b^(8 * (1/2))
This simplifies to
a^6b^4
So, the simplified version of the expression ((a^(4)b^(2))/(a^(-8)b^(-6)))^((1)/(2)) is a^6b^4.