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 is the solution to the question: 3. Evaluate and simplify: 3^(x+2) - 3^(x-1)3^x Step 1: Apply the exponent rule a^m+n = a^m · a^n and a^m-n = a^m · a^-n to the terms in the numerator. 3^(x+2) = 3^x · 3^2 3^(x-1) = 3^x · 3^-1 Step 2: Substitute these expanded terms back into the expression. 3^x · 3^2 - 3^x · 3^-13^x Step 3: Factor out the common term 3^x from the numerator. 3^x (3^2 - 3^-1)3^x Step 4: Cancel out 3^x from the numerator and the denominator. 3^2 - 3^-1 Step 5: Evaluate the powers of 3. 3^2 = 9 3^-1 = (1)/(3) Step 6: Perform the subtraction. To do this, find a common denominator. 9 - (1)/(3) = (27)/(3) - (1)/(3) (27 - 1)/(3) = (26)/(3) The simplified expression is (26)/(3). That's 2 down. 3 left today — send the next one.