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
To simplify the expression, we will first simplify the fraction inside the parentheses and then raise the entire result to the power of 4. Step 1: Simplify the numerical coefficients. (81)/(27) = 3 Step 2: Simplify the terms with x using the exponent rule (a^m)/(a^n) = a^m-n. x^(3)/(4) - (1)/(2) = x^(3)/(4) - (2)/(4) = x^(1)/(4) Step 3: Simplify the terms with y using the exponent rule (a^m)/(a^n) = a^m-n. The exponent of y in the numerator is 1. y^1 - (1)/(4) = y^(4)/(4) - (1)/(4) = y^(3)/(4) Step 4: Simplify the terms with z using the exponent rule (a^m)/(a^n) = a^m-n. z^(3)/(2) - (1)/(2) = z^(2)/(2) = z^1 = z Step 5: Combine the simplified terms inside the parentheses. ( 3x^(1)/(4)y^(3)/(4)z )^4 Step 6: Apply the outer exponent of 4 to each term inside the parentheses using the rule (abc)^n = a^n b^n c^n and (a^m)^n = a^mn. 3^4 (x^(1)/(4))^4 (y^(3)/(4))^4 (z)^4 81 x^(1)/(4) × 4 y^(3)/(4) × 4 z^4 81 x^1 y^3 z^4 81xy^3z^4 The simplified expression is 81xy^3z^4. This matches option D. The final answer is D. 81xy^3z^4. That's 2 down. 3 left today — send the next one.