Which expression is equivalent to 2, to the power minus 2 , dot, 2, to the power minus 2 , question mark2

Question

−2
⋅2
−2
?
Answer
Multiple Choice Answers
4, to the power 44
4

4, to the power minus 44
−4

2, to the power minus 42
−4

2, to the power 42
4

Answer 1

To simplify the expression \( 2^{-2} \cdot 2^{-2} \), we can apply the property of exponents that states \( a^m \cdot a^n = a^{m+n} \).

Here, we have:

\[ 2^{-2} \cdot 2^{-2} = 2^{-2 + (-2)} = 2^{-4} \]

Now, looking at the multiple-choice answers:

1. \( 4^{4} \)
2. \( 4^{-4} \)
3. \( 2^{-42} \)
4. \( 2^{42} \)

We can express \( 2^{-4} \) in a different form to match one of the choices. We know that:

\[ 4 = 2^2 \implies 4^{-4} = (2^2)^{-4} = 2^{-8} \]

None of the options provided match \( 2^{-4} \) directly.

Thus, looking closer at \( 2^{-4} \):

The closest selection that includes \( 2^{-4} \) without altering the base is not available. Therefore, none of the multiple-choice answers match the simplified expression accurately.

To summarize: The expression \( 2^{-2} \cdot 2^{-2} \) simplifies to \( 2^{-4} \). There is no equivalent match in the given options.