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: Convert all numbers to their prime bases. We have 3^x-1, which is already in base 3. ((1)/(3))^-2 = (3^-1)^-2 = 3^(-1) × (-2) = 3^2. 0.125 = (125)/(1000) = (1)/(8) = 2^-3. So, (0.125)^2x-1 = (2^-3)^2x-1 = 2^-3(2x-1) = 2^-6x+3. 27^-x+2 = (3^3)^-x+2 = 3^3(-x+2) = 3^-3x+6. Step 2: Substitute these into the expression. 3^x-1 · 3^2 · 2^-6x+33^-3x+6 Step 3: Combine terms with the same base in the numerator. Using the rule a^m · a^n = a^m+n: 3^x-1+2 · 2^-6x+33^-3x+6 = 3^x+1 · 2^-6x+33^-3x+6 Step 4: Combine terms with the same base using the division rule. Using the rule (a^m)/(a^n) = a^m-n: 3^(x+1) - (-3x+6) · 2^-6x+3 3^x+1+3x-6 · 2^-6x+3 3^4x-5 · 2^-6x+3 The simplified expression is: 3^4x-5 · 2^-6x+3 Send me the next one 📸