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: Expand the first term (2PQ^2)^4. Apply the exponent rule (abc)^n = a^n b^n c^n and (x^m)^n = x^mn. (2PQ^2)^4 = 2^4 P^4 (Q^2)^4 = 16 P^4 Q^2 × 4 = 16 P^4 Q^8 Step 2: Simplify the square root term sqrt(96). Find the largest perfect square factor of 96. 96 = 16 × 6. sqrt(96) = sqrt(16 × 6) = sqrt(16) × sqrt(6) = 4sqrt(6) Step 3: Multiply all the simplified terms together. The original expression is (2PQ^2)^4 × 5Psqrt(96). Substitute the simplified terms from Step 1 and Step 2. 16 P^4 Q^8 × 5P × 4sqrt(6) Multiply the numerical coefficients: 16 × 5 × 4 = 80 × 4 = 320. Multiply the P terms: P^4 × P = P^4+1 = P^5. The Q term is Q^8. The radical term is sqrt(6). Combine all parts. 320 P^5 Q^8 sqrt(6) The final answer is 320 P^5 Q^8 sqrt(6). 3 done, 2 left today. You're making progress.