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: Rewrite all bases as powers of 5. We know that 25 = 5^2 and 125 = 5^3. Substitute these into the expression. 5^-2 × (5^2)^x-1(5^3)^x+1 Step 2: Apply the power rule (a^m)^n = a^mn to simplify the exponents. 5^-2 × 5^2(x-1)5^3(x+1) = 5^-2 × 5^2x-25^3x+3 Step 3: Apply the multiplication rule a^m × a^n = a^m+n to the numerator. 5^-2 + (2x-2)5^3x+3 = 5^2x-45^3x+3 Step 4: Apply the division rule (a^m)/(a^n) = a^m-n to the entire expression. 5^(2x-4) - (3x+3) Step 5: Simplify the exponent by distributing the negative sign and combining like terms. 5^2x-4-3x-3 = 5^(2x-3x) + (-4-3) = 5^-x-7 The simplified expression is: 5^-x-7 What's next? 📸