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 expression inside the parenthesis by combining like terms. We use the exponent rule (a^m)/(a^n) = a^m-n. For the numerical coefficients: (4)/(16) = (1)/(4) For the x terms: (x^8)/(x^4) = x^8-4 = x^4 For the y terms: y^-6y^-4 = y^-6 - (-4) = y^-6+4 = y^-2 For the z terms (remember z = z^1): (z^1)/(z^-3) = z^1 - (-3) = z^1+3 = z^4 Combine these simplified terms: ((1)/(4) x^4 y^-2 z^4)^(1)/(2) Step 2: Apply the outer exponent (1)/(2) to each term inside the parenthesis. We use the exponent rule (ab)^n = a^n b^n and (a^m)^n = a^mn. ((1)/(4))^(1)/(2) (x^4)^(1)/(2) (y^-2)^(1)/(2) (z^4)^(1)/(2) Step 3: Evaluate each part. ((1)/(4))^(1)/(2) = sqrt((1)/(4)) = sqrt(1)sqrt(4) = (1)/(2) (x^4)^(1)/(2) = x^4 × (1)/(2) = x^2 (y^-2)^(1)/(2) = y^-2 × (1)/(2) = y^-1 (z^4)^(1)/(2) = z^4 × (1)/(2) = z^2 Step 4: Combine the results and write with positive exponents. (1)/(2) x^2 y^-1 z^2 Since y^-1 = (1)/(y), the expression becomes: (1)/(2) x^2 (1)/(y) z^2 = (x^2 z^2)/(2y) The simplified expression is: (x^2 z^2)/(2y) Got more? Send 'em