1. The problem is to simplify the expression $5^7 + 5^9$. 2. Notice that both terms have a common base of 5, so we can factor out the smallest power, which is $5^7$. 3. Factor out $5^7$: $$5^7 + 5^9 = 5^7 + 5^7 \cdot 5^2$$ 4. Simplify inside the parentheses: $$5^7 (1 + 5^2) = 5^7 (1 + 25)$$ 5. Add inside the parentheses: $$5^7 \cdot 26$$ 6. Write the final simplified expression as: $$26 \cdot 5^7$$