Question

qual o resultado simplificado da expressão: raiz quadrada da raiz cúbica da raiz quinta de m^32? 

Answer 1

$\sqrt[n]{a^{x}}=a^{x/n}$
$\sqrt[n]{x^{n}}=x$
$(a^{x})^{n}=a^{(x*n)}$
______________________________

$\sqrt{\sqrt[3]{\sqrt[5]{m^{32}}}} = (([m^{32}]^{1/5})^{1/3})^{1/2}$
$\sqrt{\sqrt[3]{\sqrt[5]{m^{32}}}} = ([m^{32}]^{1/30}$
$\sqrt{\sqrt[3]{\sqrt[5]{m^{32}}}} = m^{32/30$
$\sqrt{\sqrt[3]{\sqrt[5]{m^{32}}}} = m^{16/15}$
$\sqrt{\sqrt[3]{\sqrt[5]{m^{32}}}} = \sqrt[15]{m^{16}}$
$\sqrt{\sqrt[3]{\sqrt[5]{m^{32}}}} = \sqrt[15]{m^{15}*m}$
$\sqrt{\sqrt[3]{\sqrt[5]{m^{32}}}} = \sqrt[15]{m^{15}}*\sqrt[15]{m}$
$\sqrt{\sqrt[3]{\sqrt[5]{m^{32}}}} =m\sqrt[15]{m}$