Solve the following expression and simplify it

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:

$$\mathbf{4^{13}}$$