Simplify and express the result in exponential form :
` ((3)/( 8 ) ) ^(3) xx ( ( 3)/(8) ) ^(11)`

Answer

To simplify the expression \(\left(\frac{3}{8}\right)^{3} \times \left(\frac{3}{8}\right)^{11}\) and express the result in exponential form, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Base and Exponents**:
The expression consists of the same base, which is \(\frac{3}{8}\), and the exponents are 3 and 11.

2. **Apply the Product of Powers Rule**:
According to the product of powers rule, when multiplying two expressions with the same base, we add the exponents:
\[ a^m \times a^n = a^{m+n} \]
Here, \(a = \frac{3}{8}\), \(m = 3\), and \(n = 11\).

3. **Add the Exponents**:
Now, we add the exponents:
\[ 3 + 11 = 14 \]

4. **Write the Result in Exponential Form**:
Substitute the sum of the exponents back into the expression:
\[ \left(\frac{3}{8}\right)^{3} \times \left(\frac{3}{8}\right)^{11} = \left(\frac{3}{8}\right)^{14} \]

5. **Final Result**:
Therefore, the simplified expression in exponential form is:
\[ \left(\frac{3}{8}\right)^{14} \]