Question

Scrie cu radical(4 pe 9) la puterea -1 pe 2 ​

Answer 1

Răspuns:

$\boxed{=\frac{\sqrt{6}}{2}}$

Explicație pas cu pas:

$\displaystyle{(\sqrt{\frac{4}{9}})^{\frac{-1}{2}} = (\frac{2}{3})^{\frac{-1}{2}} }$

$\displaystyle{(\frac{3}{2})^{\frac{1}{2}} = \frac{3^{\frac{1}{2}}}{2^{\frac{1}{2}}} }$

$\displaystyle{= \frac{\sqrt{3}}{\sqrt{2}} = \frac{\sqrt{6}}{2}}$

Answer 2

Răspuns: $\bf \red{\boxed{\bf ~\dfrac{\sqrt{6}}{2}}~}$  

Explicație pas cu pas:

$\bf \bigg(\sqrt{ \dfrac{4}{9} } ~\bigg)^{\dfrac{-1~}{2}} =\bigg(\sqrt{ \dfrac{2^{2} }{3^{2} } } ~\bigg)^{\dfrac{-1~}{2}} =\bigg( \dfrac{2}{3} \bigg)^{\dfrac{-1~}{2}} =$

$\bf\bigg( \dfrac{3}{2} \bigg)^{\dfrac{1}{2}} = \dfrac{~~3^{\frac{1}{2}}~~}{~2^{\frac{1}{2}}~~}=\sqrt{\dfrac{3}{2}} =\dfrac{^{^{\sqrt{2} )}} \sqrt{3}~}{\sqrt{2}}=$

$\bf \dfrac{\sqrt{3}\cdot \sqrt{2}}{\sqrt{2}\cdot \sqrt{2}}=\red{\boxed{\bf ~\dfrac{\sqrt{6}}{2}}~}$