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
Step 1: Solve for the value of a. We are given the equation 2^a = 16. We can express 16 as a power of 2: 16 = 2 × 2 × 2 × 2 = 2^4. So, we have: 2^a = 2^4 Equating the exponents, we find: a = 4 Step 2: Solve for the value of b. We are given the equation 2^b = 4. We can express 4 as a power of 2: 4 = 2 × 2 = 2^2. So, we have: 2^b = 2^2 Equating the exponents, we find: b = 2 Step 3: Calculate the value of a-b. Now that we have the values for a and b, we can find their difference: a - b = 4 - 2 = 2 Step 4: Evaluate the expression 3^a-b. Substitute the value of a-b into the expression 3^a-b: 3^a-b = 3^2 3^2 = 3 × 3 = 9 The final answer is 9. 3 done, 2 left today. You're making progress.