Question

seja:
A = ( - 2/3)² : ( - 2/3)³  e B = ( -1/4) x ( 8/3)
 
 Calcule A x B

Answer 1

A * B


$A = (-\dfrac{2}{3})^2\ \div \ (-\dfrac{2}{3})^3 \\ \\ \\ B = (-\dfrac{1}{4}) * (\dfrac{8}{3})$

Resolver separadamente:

$A = (-\dfrac{2}{3})^2\ \div \ (-\dfrac{2}{3})^3 \\ \\ \\ A = \dfrac{4}{9}\ \div \ (-\dfrac{8}{27})$

Inverte a fração do segundo termo e passa multiplicando:

$A = \dfrac{4}{9}\ * \ (-\dfrac{27}{8}) \\ \\ \\ A = \dfrac{4 * -27}{ 9 * 8} \\ \\ \\ A = \dfrac{-108}{72} \\ \\ \\ A = \dfrac{-108}{72} \div \ \ \dfrac{36}{36} \ \ \ => -\dfrac{3}{2} \\ \\ \\ \\ A = -\dfrac{3}{2}$

==========

$B = (-\dfrac{1}{4}) * (\dfrac{8}{3}) \\ \\ \\ B =-\dfrac{1 * 8}{4 * 3} \\ \\ \\ B = -\dfrac{8}{12} \ \div \ \ \dfrac{4}{4} \ \ \ => -\dfrac{2}{3} \\ \\ \\ \\ B = -\dfrac{2}{3}$

=========================

A * B 


$-\dfrac{3}{2} * -\dfrac{2}{3} \\ \\ \\ \dfrac{-3 * 2}{-2 * 3 } \ \ => 1$


$\fbox{ \ \ A * B = \ 1 \ }$