Práctica 0 ejercicio 1l - versión 2017

EJERCICIO 1: Calcule

(l) $ \left(\dfrac{4}{9}\right)^{-\dfrac{1}{2}} + \left(\dfrac{1}{6}\right)^{\dfrac{3}{4}} $

Solución:

\begin{eqnarray*}
\left(\dfrac{4}{9}\right)^{-\dfrac{1}{2}} + \left(\dfrac{1}{6}\right)^{\dfrac{3}{4}} & = & \left(\dfrac{9}{4}\right)^{\dfrac{1}{2}} + \left(\dfrac{1}{6}\right)^{\dfrac{3}{4}} \\
& = & \left(\dfrac{\sqrt{9}}{\sqrt{4}}\right) + \left(\dfrac{1^{\frac{3}{4}}}{6^{\frac{3}{4}}}\right) \\
& = & \left(\dfrac{3}{2}\right) + \left(\dfrac{1}{\sqrt[4]{6^{3}}}\right) \\
& = & \dfrac{3}{2} + \dfrac{1}{\sqrt[4]{216}} \\
& = & \dfrac{3\sqrt[4]{216} +2}{2\sqrt[4]{216}} \\
\dfrac{3\sqrt[4]{216} +2}{2\sqrt[4]{216}} \cdot \dfrac{\sqrt[4]{216}}{\sqrt[4]{216}} \\
\end{eqnarray*}

$$\boxed{ \left(\dfrac{4}{9}\right)^{-\dfrac{1}{2}} + \left(\dfrac{1}{6}\right)^{\dfrac{3}{4}}= \dfrac{3\sqrt[4]{216} +2}{2\sqrt[4]{216}} }$$