Răspuns:
[tex]\boxed{=\frac{\sqrt{6}}{2}}[/tex]
Explicație pas cu pas:
[tex]\displaystyle{(\sqrt{\frac{4}{9}})^{\frac{-1}{2}} = (\frac{2}{3})^{\frac{-1}{2}} }[/tex]
[tex]\displaystyle{(\frac{3}{2})^{\frac{1}{2}} = \frac{3^{\frac{1}{2}}}{2^{\frac{1}{2}}} }[/tex]
[tex]\displaystyle{= \frac{\sqrt{3}}{\sqrt{2}} = \frac{\sqrt{6}}{2}}[/tex]
Răspuns: [tex]\bf \red{\boxed{\bf ~\dfrac{\sqrt{6}}{2}}~}[/tex]
Explicație pas cu pas:
[tex]\bf \bigg(\sqrt{ \dfrac{4}{9} } ~\bigg)^{\dfrac{-1~}{2}} =\bigg(\sqrt{ \dfrac{2^{2} }{3^{2} } } ~\bigg)^{\dfrac{-1~}{2}} =\bigg( \dfrac{2}{3} \bigg)^{\dfrac{-1~}{2}} =[/tex]
[tex]\bf\bigg( \dfrac{3}{2} \bigg)^{\dfrac{1}{2}} = \dfrac{~~3^{\frac{1}{2}}~~}{~2^{\frac{1}{2}}~~}=\sqrt{\dfrac{3}{2}} =\dfrac{^{^{\sqrt{2} )}} \sqrt{3}~}{\sqrt{2}}=[/tex]
[tex]\bf \dfrac{\sqrt{3}\cdot \sqrt{2}}{\sqrt{2}\cdot \sqrt{2}}=\red{\boxed{\bf ~\dfrac{\sqrt{6}}{2}}~}[/tex]
