Question Number 223822 by fantastic last updated on 06/Aug/25
$$\left(\left(\frac{\mathrm{4}}{\mathrm{3}}\right)^{\frac{\mathrm{4}}{\mathrm{3}}} \right) \\ $$$$\:{Rewrite}\:{in}\:{simplest}\:{radical}\:{form} \\ $$
Answered by Raphael254 last updated on 06/Aug/25
$$ \\ $$$$\left(\left(\frac{\mathrm{4}}{\mathrm{3}}\right)^{\frac{\mathrm{4}}{\mathrm{3}}} \right)\:=\:\sqrt[{\mathrm{3}}]{\left(\frac{\mathrm{4}}{\mathrm{3}}\right)^{\mathrm{4}} }\:=\:\sqrt[{\mathrm{3}}]{\left(\frac{\mathrm{4}}{\mathrm{3}}\right)^{\mathrm{3}} ×\left(\frac{\mathrm{4}}{\mathrm{3}}\right)}\:=\:\sqrt[{\mathrm{3}}]{\left(\frac{\mathrm{4}}{\mathrm{3}}\right)^{\mathrm{3}} }×\sqrt[{\mathrm{3}}]{\left(\frac{\mathrm{4}}{\mathrm{3}}\right)}\:=\:\left(\frac{\mathrm{4}}{\mathrm{3}}\right)×\sqrt[{\mathrm{3}}]{\left(\frac{\mathrm{4}}{\mathrm{3}}\right)}\:=\:\frac{\mathrm{4}}{\mathrm{3}}×\sqrt[{\mathrm{3}}]{\frac{\mathrm{4}}{\mathrm{3}}}\:{or}\:\frac{\mathrm{4}\sqrt[{\mathrm{3}}]{\frac{\mathrm{4}}{\mathrm{3}}}}{\mathrm{3}}\:{or}\:\frac{\mathrm{4}\sqrt[{\mathrm{3}}]{\frac{\mathrm{4}}{\mathrm{3}}}}{\mathrm{3}}×\frac{\sqrt[{\mathrm{3}}]{\mathrm{27}}}{\:\sqrt[{\mathrm{3}}]{\mathrm{27}}}\:=\:\frac{\mathrm{4}\sqrt[{\mathrm{3}}]{\frac{\mathrm{4}}{\mathrm{3}}×\mathrm{27}}}{\mathrm{3}×\mathrm{3}}\:=\:\frac{\mathrm{4}\sqrt[{\mathrm{3}}]{\mathrm{4}×\mathrm{9}}}{\mathrm{9}}\:=\:\frac{\mathrm{4}\sqrt[{\mathrm{3}}]{\mathrm{36}}}{\mathrm{9}} \\ $$
Commented by fantastic last updated on 06/Aug/25
$${thanks}\:{sir} \\ $$
Answered by mr W last updated on 06/Aug/25
$$\left(\frac{\mathrm{4}}{\mathrm{3}}\right)^{\frac{\mathrm{4}}{\mathrm{3}}} =\frac{\mathrm{4}}{\mathrm{3}}\sqrt[{\mathrm{3}}]{\frac{\mathrm{4}}{\mathrm{3}}}=\frac{\mathrm{4}\sqrt[{\mathrm{3}}]{\mathrm{36}}}{\mathrm{9}} \\ $$
Commented by fantastic last updated on 06/Aug/25
$${rigth}\:{sir} \\ $$