Here are the solutions to the problems. 2. Simplify the expression: $C^4 \times C^3 \times C^5$ Step 1: When multiplying exponents with the same base, add the powers. $$C^{4+3+5}$$ Step 2: Add the exponents. $$C^{12}$$ The simplified expression is $\boxed{C^{12}}$. 3. Simplify the expression: $2^5 \times 3^7 \times 2^{11} \times 3^6$ Step 1: Group terms with the same base. $$(2^5 \times 2^{11}) \times (3^7 \times 3^6)$$ Step 2: Apply the product rule for exponents ($a^m \times a^n = a^{m+n}$) to each base. $$2^{5+11} \times 3^{7+6}$$ Step 3: Add the exponents for each base. $$2^{16} \times 3^{13}$$ The simplified expression is $\boxed{2^{16} \times 3^{13}}$. 4. Simplify the expression: $5m^2n \times 12mn^3$ Step 1: Multiply the coefficients. $$5 \times 12 = 60$$ Step 2: Multiply the terms with base $m$. Remember $m = m^1$. $$m^2 \times m^1 = m^{2+1} = m^3$$ Step 3: Multiply the terms with base $n$. Remember $n = n^1$. $$n^1 \times n^3 = n^{1+3} = n^4$$ Step 4: Combine the results. $$60m^3n^4$$ The simplified expression is $\boxed{60m^3n^4}$. That's 2 down. 3 left today — send the next one.