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: Apply the negative exponent rule ((a)/(b))^-n = ((b)/(a))^n. ((4)/(5))^2 × 5^4 × ((5)/(2))^2 ÷ ((2)/(5))^3 Step 2: Apply the exponent rule ((a)/(b))^n = (a^n)/(b^n) and express 4 as 2^2. (4^2)/(5^2) × 5^4 × (5^2)/(2^2) ÷ (2^3)/(5^3) ((2^2)^2)/(5^2) × 5^4 × (5^2)/(2^2) ÷ (2^3)/(5^3) (2^4)/(5^2) × 5^4 × (5^2)/(2^2) ÷ (2^3)/(5^3) Step 3: Convert the division to multiplication by taking the reciprocal of the last term. (2^4)/(5^2) × 5^4 × (5^2)/(2^2) × (5^3)/(2^3) Step 4: Group terms with the same base and apply the exponent rules a^m × a^n = a^m+n and (a^m)/(a^n) = a^m-n. For base 2: (2^4)/(2^2 × 2^3) = (2^4)/(2^2+3) = (2^4)/(2^5) = 2^4-5 = 2^-1 For base 5: (5^4 × 5^2 × 5^3)/(5^2) = 5^4+2+35^2 = (5^9)/(5^2) = 5^9-2 = 5^7 Step 5: Combine the simplified terms. 2^-1 × 5^7 = (1)/(2) × 5^7 Step 6: Calculate 5^7. 5^7 = 5 × 5 × 5 × 5 × 5 × 5 × 5 = 78125 Step 7: Substitute the value and simplify. (1)/(2) × 78125 = (78125)/(2) The final answer is (78125)/(2). Send me the next one 📸