Question

2. Indique que número se obtiene luego de efectuar:
[(256)^(〖√2〗^(√2(1-√(8))) ) ]^((1/√2)^(2^(1/2) ) )

Answer 1

Respuesta:

El valor de la operación es 4

Explicación paso a paso:

$\left[(256)^{\left(\sqrt{2}\right)^{\sqrt{2}\left(1-\sqrt{8}\right)}}\right]^{\left(\frac{1}{\sqrt{2}}\right)^{2^{\frac{1}{2}}}}$

Resolvamos:

$\left[(256)^{\left(\sqrt{2}\right)^{\sqrt{2}\left(1-\sqrt{8}\right)}}\right]^{\left(\frac{1}{\sqrt{2}}\right)^{2^{\frac{1}{2}}}}\\\\\left[(256)^{\left(\sqrt{2}\right)^{\sqrt{2} -\sqrt{16} }}\right]^{\left(\frac{1}{\sqrt{2}}\right)^{2^{\frac{1}{2}}}}\\\\\left[(256)^{\left(\sqrt{2}\right)^{\sqrt{2} -4}}\right]^{\left(\frac{1}{\sqrt{2}}\right)^{2^{\frac{1}{2}}}}\\\\(256)^{(\frac{\sqrt{2}^{\sqrt{2} } }{\sqrt{2}^{4} } )} ] ^{(\frac{1}{\sqrt{2}})^{\sqrt{2} } }$

$[(256)^{(\frac{\sqrt{2}^{\sqrt{2} } }{4 } )} ] ^{(\frac{1}{\sqrt{2}^{\sqrt{2} } })$

$(256)^{\frac{1}{4} } \\\\\sqrt[4]{256} \\\\4$

Por lo tanto, el valor de la operación es 4