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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Welcome back Pookie💍🫀❤️🔥 — been a while! Let's pick up where you left off. What is a cube root? Which diagram represents this? The cube root of 27 is 3, meaning 3 × 3 × 3 = 27. This means a cube with side length 3 units. Diagram c) represents a cube made of 3 × 3 × 3 = 27 smaller cubes. The diagram that represents the cube root of 27 is c). 1. Write the following in exponential form: a) 2 × 2 Step 1: Count how many times 2 is multiplied by itself. 2 × 2 = 2^2 The exponential form is 2^2. b) 7 × 7 Step 1: Count how many times 7 is multiplied by itself. 7 × 7 = 7^2 The exponential form is 7^2. 2. Write the following as multiplication sentences: a) 12^2 Step 1: The exponent 2 means the base is multiplied by itself 2 times. 12^2 = 12 × 12 The multiplication sentence is 12 × 12. b) 7^2 Step 1: The exponent 2 means the base is multiplied by itself 2 times. 7^2 = 7 × 7 The multiplication sentence is 7 × 7. 3. Identify the following in 3^2: a) the base Step 1: In exponential notation a^b, a is the base. The base is 3. b) the exponent Step 1: In exponential notation a^b, b is the exponent. The exponent is 2. 4. Write the following in exponential form: a) 3 × 3 × 3 Step 1: Count how many times 3 is multiplied by itself. 3 × 3 × 3 = 3^3 The exponential form is 3^3. b) 2 × 2 × 2 Step 1: Count how many times 2 is multiplied by itself. 2 × 2 × 2 = 2^3 The exponential form is 2^3. 5. Expand the expression as shown in the example: a) 2^3 Step 1: The exponent 3 means the base is multiplied by itself 3 times. 2^3 = 2 × 2 × 2 The expanded expression is 2 × 2 × 2. b) 4^3 Step 1: The exponent 3 means the base is multiplied by itself 3 times. 4^3 = 4 × 4 × 4 The expanded expression is 4 × 4 × 4. 6. Calculate: a) 2^2 + 10^2 Step 1: Calculate each exponential term. 2^2 = 2 × 2 = 4 10^2 = 10 × 10 = 100 Step 2: Add the results. 4 + 100 = 104 The calculated value is 104. b) 6^2 - 3^2 Step 1: Calculate each exponential term. 6^2 = 6 × 6 = 36 3^2 = 3 × 3 = 9 Step 2: Subtract the second result from the first. 36 - 9 = 27 The calculated value is 27. Drop the next question!