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This is always true with real numbers, but not always for imaginary numbers We have ( x y) 2 = ( x y) ( x y) = x y x y = x x y y = x 2 × y 2 (xy)^2= (xy) (xy)=x {\color {#D61F06} {yx}} y=x {\color {#D61F06} {xy}}y=x^2 \times y^2\ _\square (xy)2 = (xy)(xy) = xyxy = xxyy = x2 ×y2 For noncommutative operators under some algebraicSimplify (xy^2)^3 (xy2)3 ( x y 2) 3 Apply the product rule to xy2 x y 2 x3(y2)3 x 3 ( y 2) 3 Multiply the exponents in (y2)3 ( y 2) 3 Tap for more steps Apply the power rule and multiply exponents, ( a m) n = a m n ( a m) n = a m n x 3 y 2 ⋅ 3 x 3 y 2 ⋅ 3 Multiply 2 2 by 3 3The answer is supposed to be yx^2y^3 2x , 2y x^3xy^2

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