Simplify and write in exponential form : `[(2^(3))^(2)xx3^(6)]-:5^(6)`

Answer

To simplify the expression \(\frac{(2^3)^2 \times 3^6}{5^6}\) and write it in exponential form, we can follow these steps:

### Step-by-Step Solution:

1. **Rewrite the Expression**:
Start with the given expression:
\[ \frac{(2^3)^2 \times 3^6}{5^6} \]

2. **Apply the Power of a Power Rule**:
Use the rule \((a^m)^n = a^{m \cdot n}\) to simplify \((2^3)^2\):
\[ (2^3)^2 = 2^{3 \cdot 2} = 2^6 \]
So, the expression now becomes:
\[ \frac{2^6 \times 3^6}{5^6} \]

3. **Combine the Terms in the Numerator**:
Notice that both terms in the numerator have the same exponent:
\[ 2^6 \times 3^6 = (2 \times 3)^6 = 6^6 \]
Therefore, the expression simplifies to:
\[ \frac{6^6}{5^6} \]

4. **Apply the Quotient Rule**:
Use the rule \(\frac{a^m}{b^m} = \left(\frac{a}{b}\right)^m\):
\[ \frac{6^6}{5^6} = \left(\frac{6}{5}\right)^6 \]

5. **Final Exponential Form**:
The final simplified expression in exponential form is:
\[ \left(\frac{6}{5}\right)^6 \]

### Final Answer:
\[ \left(\frac{6}{5}\right)^6 \]