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Question: Solve the following expression and simplify it: $$8^8 + 8^8 + 8^8 + 8^8 = ?$$ Solution: Step 1: Factor out the common term $$8^8 + 8^8 + 8^8 + 8^8 = 4 \times 8^8$$ Step 2: Express 8 in terms of base 2 Since $$8 = 2^3$$ , we write: $$8^8 = (2^3)^8 = 2^{24}$$ Thus, our expression becomes: $$4 \times 2^{24}$$ Step 3: Express 4 in terms of base 2 Since $$4 = 2^2$$ , we substitute: $$2^2 \times 2^{24}$$ Applying exponent rules: $$2^{2+24} = 2^{26}$$ Step 4: Convert back to base 4 Since $$4 = 2^2$$ , we rewrite: $$2^{26} = (2^2)^{13} = 4^{13}$$ Final Answer: $$\mathbf{4^{13}}$$