Question

AYUDENME POOORFAAAVOR

Answer 1

Respuesta:   $E=\frac{17161}{435600}\quad \left(\mathrm{Decimal}:\quad E=0.03939\dots \right)$

Explicación paso a paso:

$E=\frac{\left[\left(0,\:\overline{13}\right)\left(0,\:5\right)^2+\left(0,\:\overline{3}\right)^2\left(0,\:3\right)\right]^2}{\left(0,\:\overline{1}\right)^2\left(\left(2\left(3\frac{1}{3}\right)+5\left(0,\:5\right)-4\left(0,\:05\right)\right)-\left(1\frac{1}{6}-1\frac{1}{5}\right)\right)}$

Pasar los decimales periódicos o puros a fracciones y los decimales mixtos a fracción impropia:

$E=\frac{\left[\left(\frac{13}{99}\right)\left(\frac{1}{2}\right)^2+\left(\frac{1}{3}\right)^2\left(\frac{3}{10}\right)\right]^2}{\left(\frac{1}{9}\right)^2\left(\left(2\left(\frac{10}{3}\right)+5\left(\frac{1}{2}\right)-4\left(\frac{1}{20}\right)\right)-\left(\frac{7}{6}-\frac{6}{5}\right)\right)}$

$\left(\frac{1}{9}\right)^2=\frac{1}{9^2}$

$E=\frac{\left(\left(\frac{1}{2}\right)^2\frac{13}{99}+\left(\frac{1}{3}\right)^2\frac{3}{10}\right)^2}{\frac{1}{9^2}\left(2\cdot \frac{10}{3}+5\cdot \frac{1}{2}-4\cdot \frac{1}{20}-\left(\frac{7}{6}-\frac{6}{5}\right)\right)}$

$2\cdot \frac{10}{3}=\frac{20}{3}$

$5\cdot \frac{1}{2}=\frac{5}{2}$

$4\cdot \frac{1}{20}=\frac{1}{5}$

$-\left(\frac{7}{6}-\frac{6}{5}\right)=\frac{1}{30}$

Queda:

$E=\frac{\left(\left(\frac{1}{2}\right)^2\frac{13}{99}+\left(\frac{1}{3}\right)^2\frac{3}{10}\right)^2}{\frac{1}{9^2}\left(\frac{5}{2}+\frac{20}{3}+\frac{1}{30}-\frac{1}{5}\right)}$

$\left(\frac{13}{99}\left(\frac{1}{2}\right)^2+\left(\frac{1}{3}\right)^2\frac{3}{10}\right)^2=\frac{131^2}{1980^2}$

$E=\frac{\frac{131^2}{1980^2}}{\frac{1}{9^2}\left(\frac{5}{2}+\frac{20}{3}+\frac{1}{30}-\frac{1}{5}\right)}$

$\mathrm{Aplicar\:las\:propiedades\:de\:las\:fracciones}:\quad \frac{\frac{b}{c}}{a}=\frac{b}{c\:\cdot \:a}$

$E=\frac{131^2}{1980^2\cdot \frac{1}{9^2}\left(\frac{20}{3}+\frac{5}{2}-\frac{1}{5}+\frac{1}{30}\right)}$

$\mathrm{Simplificar}\:\frac{20}{3}+\frac{5}{2}-\frac{1}{5}+\frac{1}{30}\:\mathrm{en\:una\:fraccion}:\quad 9$

$E=\frac{131^2}{1980^2\cdot \:9\cdot \frac{1}{9^2}}$

$1980^2\cdot \frac{1}{9^2}\cdot \:9=35283600\cdot \frac{1}{81}$

$E=\frac{17161}{35283600\cdot \frac{1}{81}}$

$\mathrm{Multiplicar\:}35283600\cdot \frac{1}{81}\::\quad 435600$

$E=\frac{17161}{435600}$

$E=0.03939\dots$