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:

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