Question

Determine a expressao . (2×)× ÷ x quando x=√2 (2 elevado a x entre parenteses)elevado a x dividido por x quando x= raiz de 2

Answer 1

$\mathrm{k=\dfrac{1}{x}\big(2^x\big)^x\ \to\ k=\dfrac{1}{x}{\big(2\big)^{x^2}}}\\\\ \mathbf{Para\ x=\sqrt{2},\ teremos\ que:}\\\\ \mathrm{k=\dfrac{1}{\sqrt{2}}\big(2\big)^{(\sqrt{2})^2}=\dfrac{1}{\sqrt{2}}\big(2\big)^2=\dfrac{4}{\sqrt{2}}}\\\\ \mathrm{k=\dfrac{4}{\sqrt{2}}\times\dfrac{\sqrt{2}}{\sqrt{2}}=\dfrac{4\sqrt{2}}{2}\ \to\ \boxed{\mathbf{k=2\sqrt{2}}}}$