Question Number 116092 by Engr_Jidda last updated on 30/Sep/20
$${Solve}\:{for}\:{x}\:{and}\:{y}\:{if} \\ $$$${x}^{{y}} =\mathrm{36} \\ $$
Commented by MJS_new last updated on 30/Sep/20
$${x},\:{y}\:\in\mathbb{Z}? \\ $$
Commented by Engr_Jidda last updated on 30/Sep/20
$${yes}\:{sir} \\ $$
Answered by MJS_new last updated on 30/Sep/20
$$\mathrm{36}=\mathrm{2}^{\mathrm{2}} \mathrm{3}^{\mathrm{2}} \\ $$$$\mathrm{36}=\mathrm{36}^{\mathrm{1}} =\left(\pm\mathrm{6}\right)^{\mathrm{2}} \\ $$$$\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix}\:\in\left\{\begin{pmatrix}{−\mathrm{6}}\\{\mathrm{2}}\end{pmatrix}\:,\:\begin{pmatrix}{\mathrm{6}}\\{\mathrm{2}}\end{pmatrix}\:,\:\begin{pmatrix}{\mathrm{36}}\\{\mathrm{1}}\end{pmatrix}\right\} \\ $$
Commented by Engr_Jidda last updated on 30/Sep/20
$${thank}\:{you}\:{sir} \\ $$