The value of `2^(2-log_(2)^(5))` is

Options

A. (A)`4//5`
B. (B)`5//4`
C. (C)`2//5`
D. (D)`5//2`

Answer

To solve the expression \(2^{2 - \log_{2}(5)}\), we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ 2^{2 - \log_{2}(5)} \]
This can be rewritten using the properties of exponents:
\[ 2^{2} \cdot 2^{-\log_{2}(5)} \]

### Step 2: Calculate \(2^{2}\)
Now we calculate \(2^{2}\):
\[ 2^{2} = 4 \]
So, we can rewrite the expression as:
\[ 4 \cdot 2^{-\log_{2}(5)} \]

### Step 3: Simplify \(2^{-\log_{2}(5)}\)
Next, we simplify \(2^{-\log_{2}(5)}\). Using the property of logarithms, we know:
\[ a^{-\log_{a}(x)} = \frac{1}{x} \]
Thus, we have:
\[ 2^{-\log_{2}(5)} = \frac{1}{5} \]

### Step 4: Combine the results
Now we can substitute back into our expression:
\[ 4 \cdot \frac{1}{5} = \frac{4}{5} \]

### Final Answer
Thus, the value of \(2^{2 - \log_{2}(5)}\) is:
\[ \frac{4}{5} \]