Simplify the expression $(\frac{-2a^2b^{\frac{3}{4}}}{12a^3b^{\frac{1}{2}}})^2$.AlgebraExponentsSimplificationAlgebraic Expressions2025/4/211. Problem DescriptionSimplify the expression(−2a2b3412a3b12)2(\frac{-2a^2b^{\frac{3}{4}}}{12a^3b^{\frac{1}{2}}})^2(12a3b21−2a2b43)2.2. Solution StepsFirst, simplify the expression inside the parenthesis.(−2a2b3412a3b12)2=(−1a2−3b34−126)2=(−1a−1b146)2(\frac{-2a^2b^{\frac{3}{4}}}{12a^3b^{\frac{1}{2}}})^2 = (\frac{-1a^{2-3}b^{\frac{3}{4}-\frac{1}{2}}}{6})^2 = (\frac{-1a^{-1}b^{\frac{1}{4}}}{6})^2(12a3b21−2a2b43)2=(6−1a2−3b43−21)2=(6−1a−1b41)2=(−b146a)2= (\frac{-b^{\frac{1}{4}}}{6a})^2=(6a−b41)2Now, apply the power of 2 to the simplified fraction:(−b146a)2=(−b14)2(6a)2=b2436a2=b1236a2(\frac{-b^{\frac{1}{4}}}{6a})^2 = \frac{(-b^{\frac{1}{4}})^2}{(6a)^2} = \frac{b^{\frac{2}{4}}}{36a^2} = \frac{b^{\frac{1}{2}}}{36a^2}(6a−b41)2=(6a)2(−b41)2=36a2b42=36a2b213. Final Answerb1236a2\frac{b^{\frac{1}{2}}}{36a^2}36a2b21
