1. The problem is to simplify $$\frac{16^{-3}}{8^4}$$ and express the answer in exponential form with base 2. 2. Recall that 16 and 8 can be written as powers of 2: $$16 = 2^4$$ and $$8 = 2^3$$. 3. Substitute these into the expression: $$\frac{(2^4)^{-3}}{(2^3)^4}$$ 4. Apply the power of a power rule $$ (a^m)^n = a^{mn} $$: $$\frac{2^{4 \times (-3)}}{2^{3 \times 4}} = \frac{2^{-12}}{2^{12}}$$ 5. Use the quotient rule for exponents $$ \frac{a^m}{a^n} = a^{m-n} $$: $$2^{-12 - 12} = 2^{-24}$$ 6. The simplified expression in base 2 exponential form is $$\boxed{2^{-24}}$$.