Final answer:
The expression (-2^3) ^ -2 simplifies to 1/64.
Step-by-step explanation:
The expression (-2^3) ^ -2 can be simplified using the rule of exponents. First, we evaluate the exponent inside the parentheses. (-2^3) is equal to (-2) * (-2) * (-2), which equals -8. Next, we raise -8 to the power of -2, which means we invert it and square it. (-8)^-2 is equal to 1/(-8)^2 = 1/64. Therefore, the value of the expression is 1/64.