ılify: \( \begin{array}{lllll}\text { (1) } 2 p^{3} \times 8 p^{2} & \text { (2) } & 6 x^{2} y^{3} \cdot 6 x y^{4} & \text { (3) } & 2^{5} \cdot 2^{3} \cdot 2 \\ \text { (4) } 9^{4} \cdot 9^{8} \cdot 3^{2} & \text { (5) } & 7^{2} \cdot 7^{2} \cdot 7 & \text { (6) } & 7^{2}+7^{2} \\ \text { (7) } 5^{5} \cdot 5^{5} \cdot 5^{5} & \text { (8) } 12 \cdot 12^{12} & \text { (9) } 3^{13} \cdot 3^{12}\end{array} \)

Below are the step‐by‐step simplifications for each expression: (1) 2p³ × 8p²  • Multiply the numerical coefficients: 2 × 8 = 16.  • For the p terms, add exponents: p³ × p² = p^(3+2) = p⁵.  Result: 16p⁵ (2) 6x²y³ · 6xy⁴  • Multiply the coefficients: 6 × 6 = 36.  • For the x terms: x² · x = x^(2+1) = x³.  • For the y terms: y³ · y⁴ = y^(3+4) = y⁷.  Result: 36x³y⁷ (3) 2⁵ · 2³ · 2  • Express all factors as powers of 2 (note that 2 = 2¹).  • Add the exponents: 5 + 3 + 1 = 9.  Result: 2⁹ (4) 9⁴ · 9⁸ · 3²  • Combine the 9 terms: 9⁴ · 9⁸ = 9^(4+8) = 9¹².  • Rewrite 9 in terms of 3, since 9 = 3², so 9¹² = (3²)¹² = 3^(2×12) = 3²⁴.  • Multiply with 3²: 3²⁴ · 3² = 3^(24+2) = 3²⁶.  Result: 3²⁶ (5) 7² · 7² · 7  • Express 7 as 7¹ to add exponents: 2 + 2 + 1 = 5.  Result: 7⁵ (6) 7² + 7²  • Since both terms are the same, combine by addition: 7² + 7² = 2·7².  Result: 2·7² (which numerically equals 98) (7) 5⁵ · 5⁵ · 5⁵  • Add the exponents: 5 + 5 + 5 = 15.  Result: 5¹⁵ (8) 12 · 12¹²  • Write 12 as 12¹ and add exponents: 1 + 12 = 13.  Result: 12¹³ (9) 3¹³ · 3¹²  • Add the exponents for the base 3: 13 + 12 = 25.  Result: 3²⁵ Each expression has been simplified by using the rules for multiplying powers (adding the exponents for like bases) or, in the addition case, combining like terms.