To determine which of the given options is NOT equal to 4, let's evaluate each expression step-by-step:
### Option A: [tex]\( (1)^{-2} \times 2^2 \)[/tex]
1. Calculate [tex]\( (1)^{-2} \)[/tex].
- Any number raised to the power of 0 is 1.
- Therefore, [tex]\( (1)^{-2} = 1^ {-2}= 1 \)[/tex].
2. Calculate [tex]\( 2^2 \)[/tex].
- [tex]\( 2^2 = 4 \)[/tex].
3. Multiply the results from steps 1 and 2.
- [tex]\( 1 \times 4 = 4 \)[/tex].
So, [tex]\( (1)^{-2} \times 2^2 = 4 \)[/tex].
### Option B: [tex]\( (-2)^2 \)[/tex]
1. Calculate [tex]\( (-2)^2 \)[/tex].
- When a negative number is squared, the result is positive.
- [tex]\( (-2)^2 = (-2) \times (-2) = 4 \)[/tex].
So, [tex]\( (-2)^2 = 4 \)[/tex].
### Option C: [tex]\( 2^{-2} \)[/tex]
1. Calculate [tex]\( 2^{-2} \)[/tex].
- [tex]\( 2^{-2} = \frac{1}{2^2} \)[/tex].
- [tex]\( 2^2 = 4 \)[/tex].
- Therefore, [tex]\( 2^{-2} = \frac{1}{4} = 0.25 \)[/tex].
So, [tex]\( 2^{-2} = 0.25 \)[/tex], which is NOT equal to 4.
### Option D: [tex]\( 2 \times 2^1 \)[/tex]
1. Calculate [tex]\( 2^1 \)[/tex].
- [tex]\( 2^1 = 2 \)[/tex].
2. Multiply the results from step 1 by 2.
- [tex]\( 2 \times 2 = 4 \)[/tex].
So, [tex]\( 2 \times 2^1 = 4 \)[/tex].
### Conclusion
From the above evaluations, we can see that Option C, [tex]\( 2^{-2} \)[/tex], equals [tex]\( 0.25 \)[/tex], which is NOT equal to 4. Therefore, the correct answer is:
[tex]\[
\boxed{C}
\][/tex]
