Ejercicio 219

octubre 30, 2019abril 13, 2019 por Gestor Baldor

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CAPITULO XXX

TEORIA DE LOS EXPONENTES

Ejercicio 219

Expresar con exponentes positivosy simplificar:

$a^{2} b^{- 3} = \frac{a^{2}}{b^{3}}$
$3 x^{- 5} = \frac{3}{x^{5}}$
$\begin{matrix} a^{- 4} b^{- \frac{1}{2}} & = \frac{1}{a^{4} b^{\frac{1}{2}}} \\ = \frac{1}{a^{4} \sqrt{b}} \end{matrix}$
$\begin{matrix} 3 x^{- 2} y^{- \frac{1}{3}} & = \frac{3}{x^{2} y^{\frac{1}{3}}} \\ = \frac{3}{x^{2} \sqrt[3]{y}} \end{matrix}$
$\begin{matrix} m^{- \frac{1}{2}} n^{- 5} & = \frac{1}{m^{\frac{1}{2}} n^{5}} \\ = \frac{1}{\sqrt{m} n^{5}} \end{matrix}$
$a^{2} b^{- 1} c = \frac{a^{2} c}{b}$
$\begin{matrix} 4 x^{2} y^{- \frac{3}{5}} & = \frac{4 x^{2}}{y^{\frac{3}{5}}} \\ = \frac{4 x^{2}}{\sqrt[5]{y^{3}}} \end{matrix}$
$\begin{matrix} 5 a^{- \frac{1}{3}} b^{- \frac{3}{4}} c^{- 1} & = \frac{5}{a^{\frac{1}{3}} b^{\frac{3}{4}} c} \\ = \frac{5}{\sqrt[3]{a} \sqrt[4]{b^{3}} c} \end{matrix}$
$\begin{matrix} \frac{1}{2 x^{- 2}} & = \frac{1}{\frac{2}{x^{2}}} \\ = \frac{x^{2}}{2} \end{matrix}$
$\begin{matrix} \frac{3}{x^{- 1} y^{- 5}} & = \frac{3}{\frac{1}{x y^{5}}} \\ = 3 x y^{5} \end{matrix}$
$\begin{matrix} \frac{2 a^{- 2} b^{- 3}}{a^{- 4} c^{- 1}} & = \frac{\frac{2}{a^{2} b^{3}}}{\frac{1}{a^{} c}} \\ = \frac{2 a^{2} c}{b^{3}} \end{matrix}$
$\begin{matrix} \frac{x^{- 1} y^{- 2} z^{- 3}}{a^{- 2} b^{- 5} c^{- 8}} & = \frac{\frac{1}{x y^{2} z^{3}}}{\frac{1}{a^{2} b^{5} c^{8}}} \\ = \frac{a^{2} b^{5} c^{8}}{x y^{2} z^{3}} \end{matrix}$
$\begin{matrix} \frac{3 m^{- 4} n^{- \frac{1}{2}}}{8 m^{- 3} n^{- 4}} & = \frac{\frac{3}{m^{4} n^{\frac{1}{2}}}}{\frac{8}{m^{3} n^{4}}} \\ = \frac{3}{8} n^{4 - \frac{1}{2}} \\ = \frac{3}{8} n^{\frac{7}{2}} \\ = \frac{3}{8} \sqrt{n^{7}} \end{matrix}$
$\begin{matrix} \frac{4 a^{\frac{1}{2}}}{7 a^{- 4} b^{2} c^{- \frac{2}{3}}} & = \frac{4 a^{\frac{1}{2}}}{\frac{b^{2}}{7 a^{4} c^{\frac{2}{3}}}} \\ = \frac{28 a^{\frac{1}{2} + 4} c^{\frac{2}{3}}}{b^{2}} \\ = \frac{28 a^{\frac{9}{2}} c^{\frac{2}{3}}}{b^{2}} \\ = \frac{28 \sqrt{a^{9}} \sqrt[3]{c^{2}}}{b^{2}} \\ = \frac{28 a \sqrt{a^{7}} \sqrt[3]{c^{2}}}{b^{2}} \end{matrix}$
$\begin{matrix} \frac{2 m^{- 5} n^{- 7}}{a^{2} m^{3} n^{- 4}} & = \frac{2 m^{- 5 - 3} n^{- 7 + 4}}{a^{2}} \\ = \frac{2 m^{- 8} n^{- 3}}{a^{2}} \\ = \frac{2}{a^{2} m^{8} n^{3}} \end{matrix}$
$\begin{matrix} \frac{a^{- \frac{1}{2}} x^{- 2}}{3 a^{3} x^{2} y^{- 1}} & = \frac{a^{- \frac{1}{2} - 3} x^{- 2 - 2} y}{3} \\ = \frac{a^{- \frac{7}{2}} x^{- 4} y}{3} \\ = \frac{y}{3 a^{\frac{7}{2}} x^{4}} \\ = \frac{y}{3 \sqrt{a^{7}} x^{4}} \end{matrix}$
$\begin{matrix} \frac{c^{2}}{4 b^{- \frac{1}{2}} x^{3}} & = \frac{c^{2} b^{\frac{1}{2}}}{4 x^{3}} \\ = \frac{c^{2} \sqrt{b}}{4 x^{3}} \end{matrix}$
$\begin{matrix} \frac{1}{3 a^{- \frac{3}{4}} b^{- \frac{2}{5}} c^{4}} & = \frac{a^{\frac{3}{4}} b^{\frac{2}{5}}}{3 c^{4}} \\ = \frac{\sqrt[4]{a^{3}} \sqrt[5]{b^{2}}}{3 c^{4}} \end{matrix}$
$\begin{matrix} \frac{3 a^{2} m n}{a^{- 3} m^{- \frac{1}{2}} n^{- \frac{3}{4}}} & = 3 a^{2 + 3} m^{1 + \frac{1}{2}} n^{1 + \frac{3}{4}} \\ = 3 a^{5} m^{\frac{3}{2}} n^{\frac{7}{4}} \\ = 3 a^{5} \sqrt[2]{m^{3}} \sqrt[4]{n^{7}} \\ = 3 a^{5} \sqrt[2]{m^{2} . m} \sqrt[4]{n^{4} . n^{3}} \\ = 3 a^{5} m n \sqrt[2]{m} \sqrt[4]{n^{3}} \end{matrix}$
$\begin{matrix} \frac{x^{- \frac{2}{3}} y^{- \frac{3}{4}}}{x^{2} y z^{- \frac{1}{2}}} & = x^{- \frac{2}{3} - 2} y^{- \frac{3}{4} - 1} z^{\frac{1}{2}} \\ = x^{- \frac{8}{3}} y^{- \frac{7}{4}} z^{\frac{1}{2}} \\ = \frac{z^{\frac{1}{2}}}{x^{\frac{8}{3}} y^{\frac{7}{4}}} \\ = \frac{\sqrt{z}}{\sqrt[3]{x^{8}} \sqrt[4]{y^{7}}} \\ = \frac{\sqrt{z}}{\sqrt[3]{x^{5} . x^{3}} \sqrt[4]{y^{4} . y^{3}}} \\ = \frac{\sqrt{z}}{x y \sqrt[3]{x^{5}} \sqrt[4]{y^{3}}} \end{matrix}$