Evaluate : `3^(2-log_(3)5)`

Options

A. A)`9/5`
B. B)45
C. C)`5//9`
D. D)`9log_(35)`

Answer

To evaluate the expression \( 3^{2 - \log_{3}5} \), we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ 3^{2 - \log_{3}5} \]
This can be rewritten using the properties of exponents:
\[ 3^{2 - \log_{3}5} = \frac{3^2}{3^{\log_{3}5}} \]

### Step 2: Calculate \( 3^2 \)
Next, we calculate \( 3^2 \):
\[ 3^2 = 9 \]

### Step 3: Simplify \( 3^{\log_{3}5} \)
Now, we simplify \( 3^{\log_{3}5} \). By the property of logarithms, we know that:
\[ 3^{\log_{3}5} = 5 \]

### Step 4: Substitute back into the expression
Now we can substitute back into our expression:
\[ \frac{3^2}{3^{\log_{3}5}} = \frac{9}{5} \]

### Step 5: Final result
Thus, the final result of the expression \( 3^{2 - \log_{3}5} \) is:
\[ \frac{9}{5} \]

### Summary
The evaluated expression is:
\[ \boxed{\frac{9}{5}} \]