Question

Cat este 2 la puterea - 2/3?

Answer 1

 

$\displaystyle\\\text{Folosim formulele:}\\\\</p><p>a^{-b}=\frac{1}{a^b}\\\\</p><p>a^{\frac{\b1}{\b b} }=\sqrt[\b b]{a}\\\\\text{Rezolvare:}\\\\2^{\left(-\frac{\b2}{\b3}\right)}=\frac{1}{2^{\left(\frac{\b2}{\b3} \right)}}=\frac{1}{\sqrt[\b3]{2^2} }=\boxed{\frac{1}{\sqrt[\b3]{4}}}$

Answer 2

$\it 2^{-\frac{2}{3}} = (2^{-1})^{\frac{2}{3}} =\left(\dfrac{1}{2}\right)^{\dfrac{2}{3}} = \left[\left(\dfrac{1}{2}\right)^2\right]^{\dfrac{1}{3}} =\left(\dfrac{1}{4}\right)^{\dfrac{1}{3}} =\sqrt[3]{\dfrac{1}{4}}$