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: Express all numbers in the expression as powers of 2. We know that 8 = 2^3, 4 = 2^2, and 16 = 2^4. Substitute these into the expression: sqrt((2^3)^2 × (2^2)^n+1)2^2n × 2^4 Step 2: Apply the exponent rule (a^m)^n = a^mn to simplify the powers. sqrt(2^3 × 2) × 2^2(n+1)2^2n × 2^4 = sqrt(2^6 × 2^2n+2)2^2n × 2^4 Step 3: Apply the exponent rule a^m × a^n = a^m+n to combine terms in the numerator and denominator. sqrt(2^6 + (2n+2))2^2n+4 = sqrt(2^2n+8)2^2n+4 Step 4: Apply the exponent rule (a^m)/(a^n) = a^m-n to simplify the fraction inside the square root. sqrt(2^(2n+8) - (2n+4)) = sqrt(2^2n+8-2n-4) = sqrt(2^4) Step 5: Evaluate the square root. sqrt(2^4) = (2^4)^(1)/(2) = 2^4 × (1)/(2) = 2^2 Step 6: Calculate the final value. 2^2 = 4 The simplified expression is: 4 What's next? Send 'em! 📸