Question

[(2/3)^(menos)1 : 2/3 . (3/2)^(menos)3] . (2/3)^(menos)5=

por favor alguien ayudemeee

Answer 1

Respuesta:

Explicación paso a paso:

Saludos

Recuerda:

$(\frac{a}{b} )^{-c} =(\frac{b}{a} )^{c} =\frac{b^{c} }{a^{c} }$

En el problema: Calcular $((\frac{2}{3} )^{-1}$ ÷ $(\frac{2}{3})( \frac{3}{2})^{-3})(\frac{2}{3} )^{-5}$

$M=$ $((\frac{2}{3} )^{-1}$ ÷ $(\frac{2}{3})( \frac{3}{2})^{-3})(\frac{2}{3} )^{-5}$

Para hacer positivo los exponentes, invertimos las fracciones

$M=((\frac{3}{2} )$ ÷ $(\frac{2}{3} )(\frac{2}{3} )^{3} )(\frac{3}{2} )^{5}$

$M=((\frac{9}{4} )(\frac{2}{3} )^{3} )(\frac{3}{2} )^{5}$

$M=((\frac{9}{4} )(\frac{2(2^{2}) }{3(3^{2} )} ))(\frac{3(3^{4} )}{2(2^{4} )} )$

$M=((\frac{9}{4} )(\frac{2(4) }{3(9 )} ))(\frac{3(81 )}{2(16 )} )$

Simplificamos:

$M=(\frac{2}{3} )(\frac{3(81)}{2(16)} )$

Simplificamos:

$M=\frac{81}{16}$