We can simplify this expression using the laws of exponents.
First, let's rewrite (2^-2) as 1/(2^2), because a negative exponent means "take the reciprocal of the base raised to the positive exponent."
So we have:
(2^-2) (4^3) = (1/(2^2)) (4^3)
Next, we can simplify (4^3) as (2^2)^3, because 4 is equal to 2 raised to the power of 2.
So we have:
(1/(2^2)) (4^3) = (1/(2^2)) ((2^2)^3) = (1/(2^2)) (2^6)
Now, we can combine the bases of the two exponents by adding their exponents because they have the same base.
So we have:
(1/(2^2)) (2^6) = 2^(6-2) = 2^4
Therefore,
(2^-2) (4^3) = 2^4 = 16.
Thus, the simplified expression is 16.