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 your problem. Problem 2: Evaluate 64^-1/2 × 129000^2/32^-4 × 3^0 × 5^2 Assumption: The number 129000 is likely a typo and should be 729000 to allow for a simplified evaluation, as 129 is not a perfect cube. We will proceed with this assumption. Step 1: Evaluate each term in the numerator. • 64^-1/2: 64^-1/2 = (1)/(64^1/2) = (1)/(sqrt(64)) = (1)/(8) • 729000^2/3: 729000^2/3 = (729 × 1000)^2/3 = (9^3 × 10^3)^2/3 = ((9 × 10)^3)^2/3 = (90^3)^2/3 = 90^2 = 8100 The numerator is (1)/(8) × 8100 = (8100)/(8) = (2025)/(2). Step 2: Evaluate each term in the denominator. • 2^-4: 2^-4 = (1)/(2^4) = (1)/(16) • 3^0: 3^0 = 1 • 5^2: 5^2 = 25 The denominator is (1)/(16) × 1 × 25 = (25)/(16). Step 3: Divide the simplified numerator by the simplified denominator. (2025)/(2)(25)/(16) = (2025)/(2) × (16)/(25) = (2025 × 16)/(2 × 25) Simplify the fractions: = (2025)/(25) × (16)/(2) = 81 × 8 = 648 The evaluated expression is 648. 3 done, 2 left today. You're making progress.