1. The problem is to evaluate and explain the logarithmic expression $$\log_4(16^3)$$. 2. Using the power rule of logarithms, $$\log_b(a^c) = c \log_b(a)$$, we rewrite $$\log_4(16^3)$$ as $$3 \log_4(16)$$. 3. Recognize that 16 can be expressed as $$4^2$$, so we substitute: $$3 \log_4(4^2)$$. 4. Apply the power rule inside the logarithm again: $$3 \times 2 \log_4(4)$$. 5. Since $$\log_4(4) = 1$$ (because any logarithm of a base to itself equals 1), this simplifies to $$3 \times 2 \times 1$$. 6. Multiply these values to get $$6$$. **Final answer:** $$\log_4(16^3) = 6$$.