Find the value of `(10)^(200)/(10)^(196)`.

Options

A. 10000
B. 1000
C. 100
D. 100000

Answer

To solve the problem \( \frac{10^{200}}{10^{196}} \), we can use the property of exponents that states:

\[ \frac{a^m}{a^n} = a^{m-n} \]

where \( a \) is the base and \( m \) and \( n \) are the exponents.

### Step-by-Step Solution:

1. **Identify the base and exponents**:
- Here, the base \( a = 10 \), \( m = 200 \), and \( n = 196 \).

2. **Apply the exponent property**:
- Using the property mentioned, we can rewrite the expression:
\[ \frac{10^{200}}{10^{196}} = 10^{200 - 196} \]

3. **Subtract the exponents**:
- Now, calculate \( 200 - 196 \):
\[ 200 - 196 = 4 \]

4. **Write the simplified expression**:
- Substitute back into the expression:
\[ 10^{200 - 196} = 10^4 \]

5. **Calculate the final value**:
- Now, calculate \( 10^4 \):
\[ 10^4 = 10 \times 10 \times 10 \times 10 = 10000 \]

Thus, the value of \( \frac{10^{200}}{10^{196}} \) is \( 10000 \).

### Final Answer:
\[ 10000 \]