1) (2xy^0,4)³/2^0,5*x^1,75 *y^(-0,8) = (8x³y^1,2)/√2x^(1,75)y^(-0,8) =
4√2 x^(5/4)y² .
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2) √(2 -√5)² -1/(√5+2) =|2 -√5| -(√5-2)/(√5+2)(√5-2) = √5 -2 -(√5 -2) / ( (√5)² -2²) = √5 -2 -(√5 -2) =0 .
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3) (a-b)/(b^(1/3) - a^(1/3)) = -(a-b)/(∛a -∛b) =-(∛a -∛b)∛a²+∛ab +∛b²)/(∛a -∛b) = -(∛a²+∛ab +∛b²).
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4) 16x^4 =1 ;
16x^4 -1= 0 ;
(4x² -1)(4x² +1) =0 ; * * * 4x² +1 ≠ 0 * * *
4x² -1 = 0 ; * * * x = ± 1/2 * * *
4(x² -(1/2)²) =0 ;
(x -1/2)(x +1/2) =0 ;
[ x = -1/2 ; x=1/2.