Question

Se x e y são números reais tais que X= 0,25 elevado a 0,25 e y = 16 elevado a -0,125

Answer 1

$x=0,25^{0,25}=\\\\x=(\frac{1}{4})^{\frac{1}{4}}\\\\x=[(\frac{1}{2})^2]^{\frac{1}{4}}\\\\x=(\frac{1}{2})^{\frac{1}{2}}\\\\\boxed{x=\frac{1}{\sqrt{2}}}$

 E,

$y=16^{-0,125}=\\\\y=(2^4)^{-\frac{1}{8}}\\\\y=2^{-\frac{1}{2}}\\\\y=(\frac{1}{2})^{\frac{1}{2}}\\\\\boxed{y=\frac{1}{\sqrt{2}}}$

 Isto é, x = y.