1. Stating the problem: Calculate the value of the expression $$4^{2020} + 2^{2017} - 15$$. 2. Simplify expressions where possible: Note that $$4 = 2^2$$, so $$4^{2020} = (2^2)^{2020} = 2^{4040}.$$ 3. Rewrite the original expression using this simplification: $$2^{4040} + 2^{2017} - 15.$$ 4. Analyze the expression for further simplification: Since the powers $$4040$$ and $$2017$$ are different, and the terms are one large power plus another power plus a subtraction by 15, the expression cannot be simplified further in terms of combining powers. 5. Final Answer: $$\boxed{2^{4040} + 2^{2017} - 15}$$