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 comparisons: a) Step 1: Evaluate 2^2. 2^2 = 2 × 2 = 4 Step 2: Evaluate 5^2. 5^2 = 5 × 5 = 25 Step 3: Compare the values. 4 < 25 Therefore, 2^2 < 5^2. b) Step 1: Evaluate 2^5. 2^5 = 2 × 2 × 2 × 2 × 2 = 32 Step 2: Evaluate 5^2. 5^2 = 5 × 5 = 25 Step 3: Compare the values. 32 > 25 Therefore, 2^5 > 5^2. c) Step 1: Evaluate 6^3. 6^3 = 6 × 6 × 6 = 216 Step 2: Evaluate 2^3. 2^3 = 2 × 2 × 2 = 8 Step 3: Compare the values. 216 > 8 Therefore, 6^3 > 2^3. d) Step 1: Evaluate 5^2. 5^2 = 5 × 5 = 25 Step 2: Evaluate 3^3. 3^3 = 3 × 3 × 3 = 27 Step 3: Compare the values. 25 < 27 Therefore, 5^2 < 3^3. e) Step 1: Evaluate 2^0. 2^0 = 1 Step 2: Evaluate 4^0. 4^0 = 1 Step 3: Compare the values. 1 = 1 Therefore, 2^0 = 4^0. f) Step 1: Evaluate sqrt(64). sqrt(64) = 8 Step 2: Evaluate 3^2. 3^2 = 3 × 3 = 9 Step 3: Compare the values. 8 < 9 Therefore, sqrt(64) < 3^2. g) Step 1: Evaluate [3]64. [3]64 = 4 Step 2: Evaluate sqrt(64). sqrt(64) = 8 Step 3: Compare the values. 4 < 8 Therefore, [3]64 < sqrt(64). h) Step 1: Consider the first number, 3. Step 2: Estimate sqrt(284). We know that 16^2 = 256 and 17^2 = 289. Since 256 < 284 < 289, it means 16 < sqrt(284) < 17. Step 3: Compare 3 with a number between 16 and 17. 3 < sqrt(284) Therefore, 3 < sqrt(284). What's next? Send 'em! 📸