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 ( (16)/(81) )^(1)/(4). Note that 16 = 2^4 and 81 = 3^4. (16)/(81) = 2^43^4 = ( (2)/(3) )^4 ( (16)/(81) )^(1)/(4) = [ ( (2)/(3) )^4 ]^(1)/(4) = ( (2)/(3) )^4 · (1)/(4) = ( (2)/(3) )^1 = (2)/(3) Step 2: Simplify ( (9)/(16) )^(1)/(2). Note that 9 = 3^2 and 16 = 4^2. (9)/(16) = 3^24^2 = ( (3)/(4) )^2 ( (9)/(16) )^(1)/(2) = [ ( (3)/(4) )^2 ]^(1)/(2) = ( (3)/(4) )^2 · (1)/(2) = ( (3)/(4) )^1 = (3)/(4) Step 3: Multiply the results. (2)/(3) · (3)/(4) Substitute numerators and denominators: (2 · 3)/(3 · 4) Cancel common factor 3: (2)/(4) Simplify by dividing numerator and denominator by 2: (2 ÷ 2)/(4 ÷ 2) = (1)/(2) (1)/(2)