To evaluate the expression \(2^{-3} \cdot 2^{-5}\), we can use the property of exponents that states \(a^m \cdot a^n = a^{m+n}\).
Using this property, we have:
\[ 2^{-3} \cdot 2^{-5} = 2^{-3 + (-5)} = 2^{-8} \]
Now, let's write \(2^{-8}\) in a different form. We know that:
\[ 2^{-8} = \frac{1}{2^8} \]
Now, let's evaluate the given options to find the equivalent expression to \(2^{-8}\).
A. \(2^{2} \cdot 2 \) - This simplifies to \(4 \cdot 2 = 8\), which is not equal to \(2^{-8}\).
B. \(1 \cdot \frac{1}{2^{2}} \) - This equals \(\frac{1}{2^2} = \frac{1}{4}\), not \(2^{-8}\).
C. \(2^{8} \cdot 2 \) - This simplifies to \(2^{9}\), not \(2^{-8}\).
D. \(1 \cdot \frac{1}{2^{8}} \) - This equals \(\frac{1}{2^8}\), which is equal to \(2^{-8}\).
Thus, the equivalent expression to \(2^{-3} \cdot 2^{-5}\) is:
D. \(128\frac{1}{2^{8}}\).
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