Which expression is equivalent to (2^2)^-1/2^2? A. 1/16. B. 1/2. C. 1. D. 1/4
The expression (2^2)^-1/2^2 can be simplified as follows:
(2^2)^-1/2^2 = 4^-1/4^2
Since any number raised to the power of -1 is equal to its reciprocal, we can rewrite 4^-1 as 1/4:
4^-1/4^2 = 1/4/4^2
Next, we simplify 4^2:
4^2 = 16
Now we can rewrite the expression:
1/4/4^2 = 1/4/16
To divide by a fraction, we multiply by its reciprocal:
1/4/16 = 1/4 * 1/16
Multiplying the numerators and denominators gives us the final answer:
1/4 * 1/16 = 1/64
Therefore, the expression (2^2)^-1/2^2 is equivalent to 1/64, so the correct answer is D. 1/4.