Question

Como calcular a metade da raiz quadrada de 5 elevado a 50 sobre 2 elevado a 25

Answer 1

$\dfrac{1}{2} \cdot \bigg(\bigg( \dfrac{\sqrt{5} }{2}\bigg)^{50}\bigg)^{25}\\\\ = \dfrac{1}{2} \cdot \bigg(\bigg( \dfrac{5^{ \frac{1}{2} } }{2}\bigg)^{50}\bigg)^{25}\\\\\\ = \dfrac{1}{2} \cdot \bigg( \dfrac{(5^{ \frac{1}{2} })^{50} }{2^{50}}\bigg)^{25}\\\\\\ = \dfrac{1}{2} \cdot \bigg( \dfrac{5^{ \frac{1}{2}\cdot50 } }{2^{50}}\bigg)^{25}\\\\\\ = \dfrac{1}{2} \cdot \bigg( \dfrac{5^{25 } }{2^{50}}\bigg)^{25}\\\\\\ = \dfrac{1}{2} \cdot \dfrac{5^{25\cdot25 } }{2^{50\cdot25}} =$

$= \dfrac{1}{2} \cdot \dfrac{5^{625 } }{2^{1250}} \\\\\\ = \dfrac{1\cdot5^{625 } }{2 \cdot 2^{1250}}\;\; como\;\;\:a^b\cdot \:a^c=a^{b+c} \\\\\\ 2^{1250}\cdot \:2=\:2^{1+1250}=\:2^{1251}\\\\ Logo,\\\\ = \dfrac{5^{625}}{2^{1251}}$