Question

Which expression is equivalent to 2−32−52−52−3​? 

A

222^{2}22 

B

122\frac{1}{2^{2}}221​ 

C

282^{8}28 

D

128\frac{1}{2^{8}}281​ 

Answer 1

To simplify the expression \( 2^{-3} \cdot 2^{-5} \cdot 2^{-5} \cdot 2^{-3} \), we can use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \).

Combining the exponents:

\[
2^{-3} \cdot 2^{-5} \cdot 2^{-5} \cdot 2^{-3} = 2^{-3 + (-5) + (-5) + (-3)}
\]

Calculating the exponents:

\[
-3 + (-5) + (-5) + (-3) = -3 - 5 - 5 - 3 = -16
\]

Thus, the expression simplifies to:

\[
2^{-16}
\]

Now, we need to express \( 2^{-16} \) in a different form. This could be expressed as:

\[
\frac{1}{2^{16}}
\]

Now, let's analyze the options given:

A: \( 2^2 \)
B: \( \frac{1}{2^2} \)
C: \( 2^8 \)
D: \( \frac{1}{2^8} \)

None of these options directly match \( \frac{1}{2^{16}} \). There might be a possible transcription issue in the choices provided. However, the closest would be a choice that represents \( \frac{1}{2^{16}} \).

Let's assume that if there was a missing or incorrect option and that the legitimate equivalent form \( 2^{-16} \) was among the choices, none of the given options A, B, C, or D would be correct based on the outcome derived.

Thus based on provided options, there seems to be no equivalent to \( 2^{-16} \). Therefore, the answer is not listed among the choices.