Question

$\text{Tema: Fracciones}$
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Answer 1

Fracciones
Propiedades de Potencias

$\bf \left(-\dfrac{2}{3} \right)^{2} = \left(-\dfrac{2}{3} \right)* \left(-\dfrac{2}{3} \right)\\ \\ \\ \bf \left(-\dfrac{2}{3} \right)^{2} = \left(+\dfrac{2*2}{3*3} \right)\\ \\ \\ \bf \left(-\dfrac{2}{3} \right)^{2} = +\dfrac{4}{9}$

$\bf \left(\dfrac{4}{2} \right)^{3}* \left(\dfrac{4}{2} \right)^{3}= \qquad Producto\ de\ igual\ base\ se\ suman\ las \ potencias\\ \\ \\\bf \left(\dfrac{4}{2} \right)^{3}* \left(\dfrac{4}{2} \right)^{3}= \left(\dfrac{4}{2} \right)^{3+3} \\ \\ \\\bf \left(\dfrac{4}{2} \right)^{3}* \left(\dfrac{4}{2} \right)^{3}= \left(\dfrac{4}{2} \right)^{6} \\ \\ \\\bf \left(\dfrac{4}{2} \right)^{3}* \left(\dfrac{4}{2} \right)^{3}= \left(2)^{6}$

$\bf \left(\dfrac{4}{2} \right)^{3}* \left(\dfrac{4}{2} \right)^{3}=64$

$\bf \left(\dfrac{7}{3} \right)^{2}: \left(\dfrac{7}{3} \right)^{4}= \qquad Cociente\ de\ igual\ base\ se\ restan\ las \ potencias\\ \\ \\\bf \left(\dfrac{7}{3} \right)^{2}: \left(\dfrac{7}{3} \right)^{4}= \left(\dfrac{7}{3} \right)^{2-4} \\ \\ \\\bf \left(\dfrac{7}{3} \right)^{2}: \left(\dfrac{7}{3} \right)^{4}= \left(\dfrac{7}{3} \right)^{-2} \\ \\ \\\bf \left(\dfrac{7}{3} \right)^{2}* \left(\dfrac{7}{3} \right)^{4}= \left(\dfrac{3}{7}\right)^{2}=\dfrac{9}{49}$

$\bf\left( \left(\dfrac{2}{3} \right)^{2}\right)^{3} = \qquad Potencia \ de\ potencia: se \ multiplica\ los\ exponentes \\ \\ \\ \bf\left( \left(\dfrac{2}{3} \right)^{2}\right)^{3} =\bf \left(\dfrac{2}{3} \right)^{2*3} = \\ \\ \\ \bf\left( \left(\dfrac{2}{3} \right)^{2}\right)^{3} =\bf \left(\dfrac{2}{3} \right)^{6} \\ \\ \\ \bf\left( \left(\dfrac{2}{3} \right)^{2}\right)^{3} =\bf \dfrac{64}{81}$

$\bf \left(\dfrac{4}{6} \right)* \left(-\dfrac{2}{3} \right)=}\qquad Multiplicacion\ se\ resuelve\ derecho \\ \\ \\ \bf \left(\dfrac{4}{6} \right)* \left(-\dfrac{2}{3} \right)=} \left(-\dfrac{4*2}{6*3} \right)\\ \\ \\ \bf \left(\dfrac{4}{6} \right)* \left(-\dfrac{2}{3} \right)=} \left(-\dfrac{8}{18} \right)\qquad\qquad Simplificamos\\ \\ \\ \bf \left(\dfrac{4}{6} \right)* \left(-\dfrac{2}{3} \right)=} -\dfrac{4}{9}$

$\bf \left(\dfrac{2}{8} \right)+ \left(\dfrac{1}{3} \right)+\left(\dfrac{1}{8} \right)-\left(\dfrac{2}{5} \right)= \qquad Hallamos\ comun\ denominador \\ \\ \\ \bf \left(\dfrac{2*15}{8*15} \right)+ \left(\dfrac{1*40}{3*40} \right)+\left(\dfrac{1*15}{8*15} \right)-\left(\dfrac{2*24}{5*24} \right)=\\ \\ \\ \bf \left(\dfrac{30}{120} \right)+ \left(\dfrac{40}{120} \right)+\left(\dfrac{15}{120} \right)-\left(\dfrac{48}{120} \right)=\left(\dfrac{30+40+15-48}{120} \right)=\dfrac{37}{120}$

$\bf \left(\dfrac{6}{9} \right)- \left(\dfrac{4}{3} \right)+\left(\dfrac{2}{8} \right)= \qquad Hallamos\ comun\ denominador \\ \\ \\ \bf \left(\dfrac{6*8}{9*8} \right)- \left(\dfrac{4*24}{3*24} \right)+\left(\dfrac{2*9}{8*9} \right)=\\ \\ \\ \bf \left(\dfrac{48}{72} \right)- \left(\dfrac{96}{72} \right)+\left(\dfrac{18}{72} \right) \right)=\left(\dfrac{48-96+18}{72} \right)=\dfrac{-30}{72}=-\dfrac{10}{24} =-\dfrac{5}{12}$

$\bf5* \left(\dfrac{2}{9} -\dfrac{1}{4} \right)= \qquad Primero \ restamos \\ \\ \\ \bf 5*\left(\dfrac{2*4}{9*4}-\dfrac{1*9}{4*9} \right)=\\ \\ \\ \bf 5*\left(\dfrac{8}{36}-\dfrac{9}{36} \right)=\\ \\ \\ \bf 5*\left(\dfrac{8-9}{36} \right)=\\ \\ \\ \bf 5*\left(\dfrac{-1}{36} \right)=\dfrac{5*(-1)}{36}=-\dfrac{5}{36}$

$\bf \left(\dfrac{2}{8} \right)* \left(\dfrac{5}{4}+ \dfrac{2}{9} -\dfrac{12}{3} \right)= \qquad Hallamos\ comun\ denominador \\ \\ \\ \bf \left(\dfrac{2}{8} \right)* \left(\dfrac{45+8-144}{36} \right)= \\ \\ \\ \bf \left(\dfrac{2}{8} \right)* \left(\dfrac{-91}{36} \right)=-\dfrac{2*91}{8*36}=-\dfrac{182}{288}=-\dfrac{91}{144}$

Espero que te sirva, salu2!!!!