1. **State the problem:** Write $a\ 3^2 \times 3$, $b\ 7 \times 7^3$, $c\ 12 \times 12^5$, and $d\ 15^4 \times 15$ as a single power. 2. **Recall the rule for multiplying powers with the same base:** $$a^m \times a^n = a^{m+n}$$ This means when multiplying powers with the same base, add the exponents. 3. **Apply the rule to each part:** - a) $3^2 \times 3 = 3^2 \times 3^1 = 3^{2+1} = 3^3$ - b) $7 \times 7^3 = 7^1 \times 7^3 = 7^{1+3} = 7^4$ - c) $12 \times 12^5 = 12^1 \times 12^5 = 12^{1+5} = 12^6$ - d) $15^4 \times 15 = 15^4 \times 15^1 = 15^{4+1} = 15^5$ 4. **Final answers:** - a) $3^3$ - b) $7^4$ - c) $12^6$ - d) $15^5$