Ejercicio 225

octubre 30, 2019abril 13, 2019 por Gestor Baldor

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CAPITULO XXX

TEORIA DE LOS EXPONENTES

Ejercicio 225

Dividir:

$\begin{matrix} a^{2} e n t r e a^{- 2} \\ a^{2} \div a^{- 2} & = a^{2} . a^{2} \\ = a^{2 + 2} \\ = a^{4} \end{matrix}$
$\begin{matrix} x^{- 3} e n t r e x^{2} \\ x^{- 3} \div x^{2} & = x^{- 3} . x^{- 2} \\ = x^{- 3 - 2} \\ = x^{- 5} \end{matrix}$
$\begin{matrix} m^{\frac{1}{2}} e n t r e m^{- \frac{1}{4}} \\ m^{\frac{1}{2}} \div m^{- \frac{1}{4}} & = m^{\frac{1}{2}} . m^{\frac{1}{4}} \\ = m^{\frac{1}{2} + \frac{1}{4}} \\ = m^{\frac{3}{4}} \end{matrix}$
$\begin{matrix} a^{2} e n t r e a^{5} \\ a^{2} \div a^{5} & = a^{2} . a^{- 5} \\ = a^{2 - 5} \\ = a^{- 3} \end{matrix}$
$\begin{matrix} x^{- 3} e n t r e x^{- 7} \\ x^{- 3} \div x^{- 7} & = x^{- 3} . x^{7} \\ = x^{- 3 + 7} \\ = x^{4} \end{matrix}$
$\begin{matrix} a^{\frac{1}{2}} e n t r e a \\ a^{\frac{1}{2}} \div a & = a^{\frac{1}{2}} . a^{- 1} \\ = a^{\frac{1}{2} - 1} \\ = a^{- \frac{1}{2}} \end{matrix}$
$\begin{matrix} x^{- \frac{2}{3}} e n t r e x^{- \frac{1}{3}} \\ x^{- \frac{2}{3}} \div x^{- \frac{1}{3}} & = x^{- \frac{2}{3}} . x^{\frac{1}{3}} \\ = x^{- \frac{2}{3} + \frac{1}{3}} \\ = x^{- \frac{1}{3}} \end{matrix}$
$\begin{matrix} a^{\frac{2}{5}} e n t r e a^{- \frac{1}{5}} \\ a^{\frac{2}{5}} \div a^{- \frac{1}{5}} & = a^{\frac{2}{5}} . a^{\frac{1}{5}} \\ = a^{\frac{2}{5} + \frac{1}{5}} \\ = a^{\frac{3}{5}} \end{matrix}$
$\begin{matrix} m^{- \frac{3}{4}} e n t r e m^{\frac{1}{2}} \\ m^{- \frac{3}{4}} \div m^{\frac{1}{2}} & = m^{- \frac{3}{4}} . m^{- \frac{1}{2}} \\ = m^{- \frac{3}{4} - \frac{1}{2}} \\ = m^{- \frac{5}{4}} \end{matrix}$
$\begin{matrix} a^{\frac{1}{3}} e n t r e a \\ a^{\frac{1}{3}} \div a & = a^{\frac{1}{3}} . a^{- 1} \\ = a^{\frac{1}{3} - 1} \\ = a^{- \frac{2}{3}} \end{matrix}$
$\begin{matrix} 4 x^{\frac{2}{5}} e n t r e 2 x^{- \frac{1}{5}} \\ 4 x^{\frac{2}{5}} \div 2 x^{- \frac{1}{5}} & = 4 x^{\frac{2}{5}} .2 x^{\frac{1}{5}} \\ = 8 x^{\frac{2}{5} + \frac{1}{5}} \\ = 8 x^{\frac{3}{5}} \end{matrix}$
$\begin{matrix} a^{- 3} e n t r e a^{- \frac{7}{4}} \\ a^{- 3} \div a^{- \frac{7}{4}} & = a^{- 3} . a^{\frac{7}{4}} \\ = a^{- 3 + \frac{7}{4}} \\ = a^{- \frac{5}{4}} \end{matrix}$
$\begin{matrix} x^{- 2} y^{- 1} e n t r e x^{- 3} y^{- 2} \\ x^{- 2} y^{- 1} \div x^{- 3} y^{- 2} & = x^{- 2} y^{- 1} . x^{3} y^{2} \\ = x^{3 - 2} y^{2 - 1} \\ = x y \end{matrix}$
$\begin{matrix} a^{\frac{1}{2}} b^{\frac{1}{3}} e n t r e a b \\ a^{\frac{1}{2}} b^{\frac{1}{3}} \div a b & = a^{\frac{1}{2}} b^{\frac{1}{3}} . a^{- 1} b^{- 1} \\ = a^{\frac{1}{2} - 1} b^{\frac{1}{3} - 1} \\ = a^{- \frac{1}{2}} b^{- \frac{2}{3}} \end{matrix}$
$\begin{matrix} a^{2} b^{- 3} e n t r e a^{- 1} b \\ a^{2} b^{- 3} \div a^{- 1} b & = a^{2} b^{- 3} . a b^{- 1} \\ = a^{2 + 1} b^{- 3 - 1} \\ = a^{3} b^{- 4} \end{matrix}$
$\begin{matrix} x^{- \frac{1}{2}} y^{- \frac{2}{3}} e n t r e x^{- \frac{1}{2}} y^{- 1} \\ x^{- \frac{1}{2}} y^{- \frac{2}{3}} \div x^{- \frac{1}{2}} y^{- 1} & = x^{- \frac{1}{2}} y^{- \frac{2}{3}} . x^{\frac{1}{2}} y \\ = x^{- \frac{1}{2} + \frac{1}{2}} y^{- \frac{2}{3} + 1} \\ = y^{\frac{1}{3}} \end{matrix}$
$\begin{matrix} m^{\frac{3}{4}} n^{- \frac{3}{4}} e n t r e m^{- \frac{1}{2}} n^{\frac{3}{4}} \\ m^{\frac{3}{4}} n^{- \frac{3}{4}} \div m^{- \frac{1}{2}} n^{\frac{3}{4}} & = m^{\frac{3}{4}} n^{- \frac{3}{4}} . m^{\frac{1}{2}} n^{- \frac{3}{4}} \\ = m^{\frac{3}{4} + \frac{1}{2}} n^{- \frac{3}{4} - \frac{3}{4}} \\ = m^{\frac{5}{4}} n^{- \frac{3}{2}} \end{matrix}$
$\begin{matrix} 8 x^{- 2} y^{\frac{2}{5}} e n t r e 4 x y^{- \frac{1}{5}} \\ 8 x^{- 2} y^{\frac{2}{5}} \div 4 x y^{- \frac{1}{5}} & = 8 x^{- 2} y^{\frac{2}{5}} .4 x^{- 1} y^{\frac{1}{5}} \\ = 32 x^{- 2 - 1} y^{\frac{2}{5} + \frac{1}{5}} \\ = 32 x^{- 3} y^{\frac{3}{5}} \end{matrix}$
$\begin{matrix} a^{\frac{1}{3}} b e n t r e a^{- \frac{1}{4}} b^{- 3} \\ a^{\frac{1}{3}} b \div a^{- \frac{1}{4}} b^{- 3} & = a^{\frac{1}{3}} b . a^{\frac{1}{4}} b^{3} \\ = a^{\frac{1}{3} + \frac{1}{4}} b^{1 + 3} \\ = a^{\frac{7}{12}} b^{4} \end{matrix}$
$\begin{matrix} x^{- 4} y^{- 5} e n t r e x^{2} y^{- 1} \\ x^{- 4} y^{- 5} \div x^{2} y^{- 1} & = x^{- 4} y^{- 5} . x^{- 2} y \\ = x^{- 4 - 2} y^{- 5 + 1} \\ = x^{- 6} y^{- 4} \end{matrix}$