![Simplify the expression [(21)/(3) x 8^(2)/(3) x 6^(5)/(4) x 3^(3)/(4)9-1 x [3]16]^-4 to find the value of x.](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1779357482956-fa8644bc71002164.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
You're on a roll — To find the value of x, we need to simplify the expression using the rules of exponents. The given expression is: x = [(2^1)/(3) × 8^(2)/(3) × 6^(5)/(4) × 3^(3)/(4)9^-1 × [3]16]^-4 Step 1: Express all numbers as powers of their prime factors (2 and 3). 8 = 2^3 6 = 2 × 3 9 = 3^2 [3]16 = 16^(1)/(3) = (2^4)^(1)/(3) = 2^(4)/(3) Step 2: Substitute these prime factor expressions into the equation. x = [(2^1)/(3) × (2^3)^(2)/(3) × (2 × 3)^(5)/(4) × 3^(3)/(4)(3^2)^-1 × 2^(4)/(3)]^-4 Step 3: Apply exponent rules (a^m)^n = a^mn and (ab)^n = a^n b^n to simplify terms. x = [(2^1)/(3) × 2^3 × (2)/(3) × 2^(5)/(4) × 3^(5)/(4) ×