Which expression is equivalent to left parenthesis, 2, to the power minus 6 , right parenthesis, squared, question mark(2

Question

−6
)
2
?
Answer
Multiple Choice Answers
2, to the power minus 42
−4

2, to the power minus 122
−12

2, to the power minus 62
−6

2, to the power 122
12

Answer 1

To simplify the expression \((2^{-6})^2\), we can use the power of a power property in exponents, which states that \((a^m)^n = a^{m \cdot n}\).

Applying this property, we have:

\[ (2^{-6})^2 = 2^{-6 \cdot 2} = 2^{-12} \]

Now let's look at the multiple-choice answers given:

1. \(2^{-42}\)
2. \(2^{-12}\)
3. \(2^{-6}\)
4. \(2^{12}\)

The expression \(2^{-12}\) matches with option 2.

Thus, the equivalent expression for \((2^{-6})^2\) is:

\[ \boxed{2^{-12}} \]