1. The problem asks to express $7^8 + 7^5$ in index form. 2. Recall the index laws: when adding powers with the same base, you cannot combine the exponents directly. You can only factor out the common base with the lowest exponent. 3. Factor out $7^5$ from both terms: $$7^8 + 7^5 = 7^5 \times 7^{8-5} + 7^5 = 7^5(7^3 + 1)$$ 4. Simplify inside the parentheses: $$7^3 = 343$$ So, $$7^5(343 + 1) = 7^5 \times 344$$ 5. The expression in index form with a common factor is: $$7^5(7^3 + 1)$$ This is the simplest index form for the sum.