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: Express the bases as powers of prime numbers. We have 243 = 3^5, 125 = 5^3, and 9 = 3^2. Step 2: Substitute these into the expression. ((3^5)^-2)/(5) × (5^3)^(2)/(3)(3^2)^-(3)/(2) Step 3: Apply the power rule (a^m)^n = a^mn to each term. For the numerator: (3^5)^-(2)/(5) = 3^5 × (-(2)/(5)) = 3^-2 (5^3)^(2)/(3) = 5^3 × ((2)/(3)) = 5^2 For the denominator: (3^2)^-(3)/(2) = 3^2 × (-(3)/(2)) = 3^-3 Step 4: Rewrite the expression with the simplified terms. 3^-2 × 5^23^-3 Step 5: Simplify the terms with the same base using the rule (a^m)/(a^n) = a^m-n. 3^-2 - (-3) × 5^2 3^-2 + 3 × 5^2 3^1 × 5^2 Step 6: Calculate the values. 3^1 = 3 5^2 = 25 Step 7: Multiply the results. 3 × 25 = 75 The simplified expression is: 75 Send me the next one 📸