This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the prime factorizations in exponential notation for each number: i) 900 Step 1: Find the prime factors of 900. 900 = 2 × 450 450 = 2 × 225 225 = 3 × 75 75 = 3 × 25 25 = 5 × 5 Step 2: Collect the prime factors and write them in exponential form. 900 = 2 × 2 × 3 × 3 × 5 × 5 = 2^2 × 3^2 × 5^2 The exponential notation is 2^2 × 3^2 × 5^2. ii) 810 Step 1: Find the prime factors of 810. 810 = 2 × 405 405 = 3 × 135 135 = 3 × 45 45 = 3 × 15 15 = 3 × 5 Step 2: Collect the prime factors and write them in exponential form. 810 = 2 × 3 × 3 × 3 × 3 × 5 = 2^1 × 3^4 × 5^1 The exponential notation is 2 × 3^4 × 5. iii) 4725 Step 1: Find the prime factors of 4725. 4725 = 3 × 1575 1575 = 3 × 525 525 = 3 × 175 175 = 5 × 35 35 = 5 × 7 Step 2: Collect the prime factors and write them in exponential form. 4725 = 3 × 3 × 3 × 5 × 5 × 7 = 3^3 × 5^2 × 7^1 The exponential notation is 3^3 × 5^2 × 7. iv) 7500 Step 1: Find the prime factors of 7500. 7500 = 2 × 3750 3750 = 2 × 1875 1875 = 3 × 625 625 = 5 × 125 125 = 5 × 25 25 = 5 × 5 Step 2: Collect the prime factors and write them in exponential form. 7500 = 2 × 2 × 3 × 5 × 5 × 5 × 5 = 2^2 × 3^1 × 5^4 The exponential notation is 2^2 × 3 × 5^4. 3 done, 2 left today. You're making progress.