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: Simplify each term in the numerator. The numerator is 64^(2)/(3) × [3]125 × (2 × (1)/(5))^-3. Simplify each part: 64^(2)/(3) = (4^3)^(2)/(3) = 4^3 × (2)/(3) = 4^2 = 16 [3]125 = [3]5^3 = 5 (2 × (1)/(5))^-3 = ((2)/(5))^-3 = ((5)/(2))^3 = (5^3)/(2^3) = (125)/(8) Multiply these simplified terms to get the numerator's value: 16 × 5 × (125)/(8) = 80 × (125)/(8) = (80)/(8) × 125 = 10 × 125 = 1250 Step 2: Simplify each term in the denominator. The denominator is 4^2 × [4]625. Simplify each part: 4^2 = 16 [4]625 = [4]5^4 = 5 Multiply these simplified terms to get the denominator's value: 16 × 5 = 80 Step 3: Divide the simplified numerator by the simplified denominator. (1250)/(80) Simplify the fraction by dividing both numerator and denominator by 10: (125)/(8) This fraction cannot be simplified further. The final answer is (125)/(8). 3 done, 2 left today. You're making progress.