Which is equivalent to left-parenthesis 2 Superscript negative 3 Baseline right-parenthesis Supescript 4 Baseline?
Answer options with 4 options
A.
negative 2 Superscript 12 Baseline
B.
StartFraction 1 over 2 Superscript 12 Baseline EndFraction
C.
StartFraction 1 over 2 Superscript 7 Baseline EndFraction
D.
2
C. StartFraction 1 over 2 Superscript 7 Baseline EndFraction
Use the shape to answer the question.
Information
The shape shows an irregular polygon comprised of two right triangles and two rectangles.
Question
What is the area of the shape?
Answer options with 5 options
A.
26 square centimeters
D.
44 square centimeters
B.
32 square centimeters
E.
60 square centimeters
C.
40 square centimeters
B. 32 square centimeters
To determine the equivalent expression for \(2^{-3^{4}}\), we need to simplify the exponentiation operations step by step.
Step 1: Evaluate the exponent \(3^{4}\).
\(3^{4} = 81\).
Step 2: Substitute the simplified exponent into the expression.
\(2^{-3^{4}} = 2^{-81}\).
At this point, we can express \(2^{-81}\) in terms of one of the given options.
Let's evaluate the options:
A. Negative 2 Superscript 12 Baseline: \( -2^{12} \)
B. StartFraction 1 over 2 Superscript 12 Baseline EndFraction: \( \frac{1}{2^{12}} \)
C. StartFraction 1 over 2 Superscript 7 Baseline EndFraction: \( \frac{1}{2^{7}} \)
D. 2: \( 2 \)
None of the given options match \(2^{-81}\).
Therefore, none of the given options is equivalent to \(2^{-3^{4}}\).