1. Problem: Simplify $ (a^5 b^9)(a^{11} b) $. 2. Use the product of powers rule: $ x^m \cdot x^n = x^{m+n} $. 3. Apply the rule to each variable: $$ a^5 \cdot a^{11} = a^{5+11} = a^{16} $$ $$ b^9 \cdot b^1 = b^{9+1} = b^{10} $$ 4. Final simplified expression: $$ a^{16} b^{10} $$ This means when multiplying powers with the same base, add their exponents. q_count is 25 because there are 25 problems in total, but only the first is solved here.