Question

Which expression is equivalent to 2-3 2-5


?
A
222^{2}2
2

B
122\frac{1}{2^{2}}
2
2

1
​

C
282^{8}2
8

D
128\frac{1}{2^{8}}
2
8

1
​

Answer 1

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. \(128\frac{1}{2^{8}}\)**.