d) $$ \left(2^{6} \div 2^{8}\right)^{3} $$

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To simplify the expression $$ \left(2^{6} \div 2^{8}\right)^{3} $$, follow these steps:

1. **Simplify the Division Inside the Parentheses:**
   
   When dividing powers with the same base, subtract the exponents:
   
   $$
   2^{6} \div 2^{8} = 2^{6 - 8} = 2^{-2}
   $$
   
   A negative exponent indicates the reciprocal:
   
   $$
   2^{-2} = \frac{1}{2^{2}} = \frac{1}{4}
   $$

2. **Raise the Result to the Power of 3:**
   
   Now, take the simplified result and raise it to the third power:
   
   $$
   \left(\frac{1}{4}\right)^{3} = \frac{1}{4^{3}} = \frac{1}{64}
   $$

**Final Answer:**

$$
\boxed{\dfrac{1}{64}}
$$
$$ \left(2^{6} \div 2^{8}\right)^{3} = \frac{1}{64} $$

d) \( \left(2^{6} \div 2^{8}\right)^{3} \)

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