1) 27^(-²/₃) +81^(³/₄) +(0.25)⁻² =
= (3³)^(-²/₃) +(3⁴)^(³/₄) +(¹/₄)⁻² =
=3⁻² + 3³ + 4² =
= ¹/₉ + 27 +16 =
= 43 ¹/₉
2) ( x² +y² - x+y ) xy⁻¹ =
( xy^(¹/₂)+x^(³/₂) y^(¹/₂)+x^(¹/₂) )
=( x² +y² - x(x+y) ) * x =
( x(y^(¹/₂)+x^(¹/₂)) x(y^(¹/₂)+x^(¹/₂)) ) y
= x² +y² -x² -xy * x =
x(y^(¹/₂) +x^(¹/₂)) y
= y(y-x) =
y(y^(¹/₂) + x^(¹/₂))
= (y^(¹/₂) - x^(¹/₂))(y^(¹/₂)+x^(¹/₂)) =
y^(¹/₂) + x^(¹/₂)
= y^(¹/₂) - x^(¹/₂) = √y - √x