Question

Упростите выражения:
$\displaystyle \boxed{1.} \frac{a^{\sqrt 5}-b^{\sqrt 7}}{a^{\frac{2 \sqrt 5}{3}}+a^{\frac{\sqrt 5}{3}}b^{\frac{\sqrt 7}{3}}+b^{\frac{2 \sqrt 7}{3}}}$

$\boxed{2.} \sqrt{(x^{\pi}+y^{\pi})^2-(4^{\frac{1}{ \pi}}xy)^{\pi}}$

Answer 1

1)
$\frac{ {a}^{ \sqrt{5} } - {b}^{ \sqrt{7} } }{ {a}^{ \frac{2 \sqrt{5} }{3} } + {a}^{ \frac{ \sqrt{5} }{3} } {b}^{ \frac{ \sqrt{7} }{3} } + {b}^{ \frac{ 2\sqrt{7} }{3} } } = \frac{( {a}^{ \frac{ \sqrt{5} }{3} } - {b}^{ \frac{ \sqrt{7} }{3} } )( {a}^{ \frac{2 \sqrt{5} }{3} } + {a}^{ \frac{ \sqrt{5} }{3} } {b}^{ \frac{ \sqrt{7} }{3} } + {b}^{ \frac{2 \sqrt{7} }{3} } )}{{a}^{ \frac{2 \sqrt{5} }{3} } + {a}^{ \frac{ \sqrt{5} }{3} } {b}^{ \frac{ \sqrt{7} }{3} } + {b}^{ \frac{ 2\sqrt{7} }{3} } } = {a}^{ \frac{ \sqrt{5} }{3} } - {b}^{ \frac{ \sqrt{7} }{3} }$
2)
$\sqrt{( {x}^{\pi} + {y}^{\pi} ) ^{2} - ( {4}^{ \frac{1}{\pi} } xy) ^{\pi} )} = \sqrt{ {x}^{2\pi} + 2 {x}^{\pi} {y}^{\pi} + {y}^{2\pi} - 4 {x}^{\pi} {y}^{\pi} )} = \sqrt{ {x}^{2\pi} - 2 {x}^{\pi} {y}^{\pi} + {y}^{2\pi} } = \sqrt{ {( {x}^{\pi} - {y}^{\pi}) }^{2} } =$
= | x^pi - y^pi |.