![Simplify the expression: ([9]512 x [3]343 x sqrt(121)) / ((64)^(1)/(3) x (81)^(3)/(4) x (14641)^(1)/(4))](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1776566907406-8f4d401ff906c0be.png&w=3840&q=75)
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 [9]512 × [3]343 × sqrt(121). We find the roots: [9]512 = [9]2^9 = 2 [3]343 = [3]7^3 = 7 sqrt(121) = sqrt(11^2) = 11 Multiply these values to get the numerator's value: 2 × 7 × 11 = 14 × 11 = 154 Step 2: Simplify each term in the denominator. The denominator is (64)^(1)/(3) × (81)^(3)/(4) × (14641)^(1)/(4). We simplify each term using exponent rules (a^m)^n = a^mn: (64)^(1)/(3) = (4^3)^(1)/(3) = 4^3 × (1)/(3) = 4^1 = 4 (81)^(3)/(4) = (3^4)^(3)/(4) = 3^4 × (3)/(4) = 3^3 = 27 (14641)^(1)/(4) = (11^4)^(1)/(4) = 11^4 × (1)/(4) = 11^1 = 11 Multiply these values to get the denominator's value: 4 × 27 × 11 = 108 × 11 = 1188 Step 3: Divide the simplified numerator by the simplified denominator. (154)/(1188) Simplify the fraction by dividing both numerator and denominator by their greatest common divisor. Both are divisible by 11: (154 ÷ 11)/(1188 ÷ 11) = (14)/(108) Both are divisible by 2: (14 ÷ 2)/(108 ÷ 2) = (7)/(54) The final answer is (7)/(54). Send me the next one 📸