![Simplify (24 imes 36)^ rac12 imes [3]8 x sqrt(81) / (16^ rac34 imes 27^ rac13).](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1776567125959-65ded65264e2de95.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 the numerator. The numerator is (2^4 × 36)^(1)/(2) × [3]8 × sqrt(81). Simplify each part: (2^4 × 36)^(1)/(2) = (2^4)^(1)/(2) × (36)^(1)/(2) = 2^4 × (1)/(2) × sqrt(36) = 2^2 × 6 = 4 × 6 = 24 [3]8 = [3]2^3 = 2 sqrt(81) = sqrt(9^2) = 9 Multiply these simplified terms to get the numerator's value: 24 × 2 × 9 = 48 × 9 = 432 Step 2: Simplify the denominator. The denominator is 16^(3)/(4) × 27^(1)/(3). Simplify each part: 16^(3)/(4) = (2^4)^(3)/(4) = 2^4 × (3)/(4) = 2^3 = 8 27^(1)/(3) = (3^3)^(1)/(3) = 3^3 × (1)/(3) = 3^1 = 3 Multiply these simplified terms to get the denominator's value: 8 × 3 = 24 Step 3: Divide the simplified numerator by the simplified denominator. (432)/(24) Perform the division: 432 ÷ 24 = 18 The final answer is 18. That's 2 down. 3 left today — send the next one.