Simplify and write in exponential form : `(3xx7^(2)xx11^(8))/(21xx11^(3))`

Options

A. `7xx11^(3)`
B. `7xx11^(5)`
C. `7xx11^(6)`
D. `7xx11^(9)`

Answer

To simplify the expression \((3 \times 7^{2} \times 11^{8})/(21 \times 11^{3})\) and write it in exponential form, we can follow these steps:

### Step-by-Step Solution:

1. **Rewrite the expression**:
\[ \frac{3 \times 7^{2} \times 11^{8}}{21 \times 11^{3}} \]

2. **Factor out the denominator**:
Notice that \(21\) can be expressed as \(3 \times 7\). So we can rewrite the denominator:
\[ 21 = 3 \times 7 \]
Therefore, the expression becomes:
\[ \frac{3 \times 7^{2} \times 11^{8}}{3 \times 7 \times 11^{3}} \]

3. **Cancel common factors**:
We can cancel \(3\) from the numerator and denominator:
\[ \frac{7^{2} \times 11^{8}}{7 \times 11^{3}} \]

4. **Simplify the expression**:
Now we can simplify \(7^{2}/7\) and \(11^{8}/11^{3}\):
\[ 7^{2}/7 = 7^{2-1} = 7^{1} = 7 \]
\[ 11^{8}/11^{3} = 11^{8-3} = 11^{5} \]

5. **Combine the results**:
Now we combine the simplified terms:
\[ 7 \times 11^{5} \]

6. **Final answer**:
Thus, the simplified expression in exponential form is:
\[ 7 \times 11^{5} \]

### Final Result:
\[ 7 \times 11^{5} \]