The value of `99(95)/(99)xx99` is

Options

A. 9798
B. 9997
C. 9898
D. 9896

Answer

To solve the expression \( \frac{99^{95}}{99} \times 99 \), we can follow these steps:

### Step 1: Simplify the Expression
The expression can be rewritten as:
\[ \frac{99^{95}}{99} \times 99 = 99^{95 - 1} \times 99 = 99^{94} \times 99 \]
This simplifies to:
\[ 99^{95} \]

### Step 2: Rewrite Using Exponent Rules
Now we can express \( 99^{95} \) in a more manageable form:
\[ 99^{95} = 99^{94} \times 99^1 = 99^{95} \]

### Step 3: Calculate \( 99^{95} \)
To find \( 99^{95} \), we can use the binomial expansion:
\[ 99^{95} = (100 - 1)^{95} \]
Using the binomial theorem, we can expand this:
\[ (100 - 1)^{95} = \sum_{k=0}^{95} \binom{95}{k} 100^{95-k} (-1)^k \]

### Step 4: Focus on the Leading Terms
For large \( n \), the leading term (when \( k = 0 \)) will dominate:
\[ 100^{95} - \binom{95}{1} 100^{94} + \text{(smaller terms)} \]

Calculating the first two terms:
- The first term is \( 100^{95} = 10^{190} \).
- The second term is \( 95 \times 100^{94} = 95 \times 10^{188} \).

### Step 5: Combine the Terms
Thus, we can approximate:
\[ 99^{95} \approx 10^{190} - 95 \times 10^{188} \]

### Step 6: Final Calculation
The final value can be calculated as:
\[ 99^{95} \approx 10^{190} - 9.5 \times 10^{189} \]
This gives us a very large number, but for practical purposes, we can round it to:
\[ 99^{95} \approx 10^{190} \]

### Final Answer
The value of \( \frac{99^{95}}{99} \times 99 \) is approximately \( 10^{190} \).

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