Evaluate :
(i) `(2^(38) + 2^(37) + 2^(36))/(2^(39) + 2^(38) + 2^(37))` (ii) `[(64^((1)/(2)))^((1)/(6))]^(2)`

Answer

Let's solve the given problems step by step.

### Part (i): Evaluate \((2^{38} + 2^{37} + 2^{36})/(2^{39} + 2^{38} + 2^{37})\)

1. **Identify the minimum power**:
- In the numerator, the minimum power is \(2^{36}\).
- In the denominator, the minimum power is \(2^{37}\).

2. **Factor out the minimum power from the numerator**:
\[ 2^{38} + 2^{37} + 2^{36} = 2^{36}(2^{2} + 2^{1} + 1) \]

3. **Factor out the minimum power from the denominator**:
\[ 2^{39} + 2^{38} + 2^{37} = 2^{37}(2^{2} + 2^{1} + 1) \]

4. **Rewrite the expression**:
\[ \frac{2^{36}(2^{2} + 2^{1} + 1)}{2^{37}(2^{2} + 2^{1} + 1)} \]

5. **Cancel the common terms**:
\[ = \frac{2^{36}}{2^{37}} = \frac{1}{2} \]

Thus, the final answer for part (i) is:
\[ \frac{1}{2} \]