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.
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Hey Faith — ready when you are. Here are the solutions to your homework and classwork problems. Homework (09/02/2026) Compare these calculations: a) Step 1: Calculate 2^2. 2^2 = 2 × 2 = 4 Step 2: Calculate 2 × 2. 2 × 2 = 4 Step 3: Compare the results. 4 = 4 So, 2^2 = 2 × 2. b) Step 1: Calculate 5^2. 5^2 = 5 × 5 = 25 Step 2: Calculate 5 × 2. 5 × 2 = 10 Step 3: Compare the results. 25 > 10 So, 5^2 > 5 × 2. c) Step 1: Calculate 9^2. 9^2 = 9 × 9 = 81 Step 2: Calculate 9 × 2. 9 × 2 = 18 Step 3: Compare the results. 81 > 18 So, 9^2 > 9 × 2. Classwork (10 April 2026) Write the next three numbers in this cubic pattern: 1, 8, 27 The pattern shows cubic numbers: 1 = 1^3 8 = 2^3 27 = 3^3 The next three numbers will be 4^3, 5^3, and 6^3. Step 1: Calculate 4^3. 4^3 = 4 × 4 × 4 = 64 Step 2: Calculate 5^3. 5^3 = 5 × 5 × 5 = 125 Step 3: Calculate 6^3. 6^3 = 6 × 6 × 6 = 216 The next three numbers are 64, 125, 216. Homework (10 April 2026) 1. Calculate and fill in <, >, =: a) 2^3 ? 2 × 3 Step 1: Calculate 2^3. 2^3 = 2 × 2 × 2 = 8 Step 2: Calculate 2 × 3. 2 × 3 = 6 Step 3: Compare the results. 8 > 6 So, 2^3 > 2 × 3. b) 1^3 ? 1 × 1 × 1 Step 1: Calculate 1^3. 1^3 = 1 × 1 × 1 = 1 Step 2: Calculate 1 × 1 × 1. 1 × 1 × 1 = 1 Step 3: Compare the results. 1 = 1 So, 1^3 = 1 × 1 × 1. c) 125 ? 5^3 Step 1: Calculate 5^3. 5^3 = 5 × 5 × 5 = 125 Step 2: Compare the results. 125 = 125 So, 125 = 5^3. Classwork (13 April 2026) 1. Calculate the cube roots: a) [3]27 Step 1: Find a number that, when multiplied by itself three times, equals 27. 3 × 3 × 3 = 27 So, [3]27 = 3. b) [3]125 Step 1: Find a number that, when multiplied by itself three times, equals 125. 5 × 5 × 5 = 125 So, [3]125 = 5. Homework (13 April 2026) 2. Calculate the square roots: a) sqrt(4) Step 1: Find a number that, when multiplied by itself, equals 4. 2 × 2 = 4 So, sqrt(4) = 2. b) sqrt(16) Step 1: Find a number that, when multiplied by itself, equals 16. 4 × 4 = 16 So, sqrt(16) = 4. c) sqrt(100) Step 1: Find a number that, when multiplied by itself, equals 100. 10 × 10 = 100 So, sqrt(100) = 10. Send me the next one 📸