Question

Scrieti rezolvarea in detaliat va rog.

Answer 1

$\displaystyle \left[\left( \frac{3}{5} \right)^6:\left(5-4 \frac{2}{5} \right)^4+2:1 \frac{1}{4} -\left( \frac{3}{5} \right)^2\right]:1 \frac{3}{5}= \\ \\ =\left[\left( \frac{3}{5} \right)^6:\left(5- \frac{5 \cdot4+2}{5} \right)^4+2: \frac{4 \cdot 1+1}{4} -\left( \frac{3}{5} \right)^2\right]: \frac{5 \cdot 1+3}{5} =$
$\displaystyle =\left[\left( \frac{3}{5} \right)^6:\left(5- \frac{20+2}{5} \right)^4+2: \frac{4+1}{4} -\left( \frac{3}{5} \right)^2\right]: \frac{5+3}{5} = \\ \\ =\left[\left( \frac{3}{5} \right)^6:\left(5- \frac{22}{5} \right)^4+2: \frac{5}{4} -\left( \frac{3}{5} \right)^2\right]: \frac{8}{5} =$
$\displaystyle =\left[\left( \frac{3}{5} \right)^6:\left( \frac{25-22}{5}\right)^4 +2 \cdot \frac{4}{5} -\left( \frac{3}{5} \right)^2\right]\cdot \frac{5}{8} = \\ \\ =\left[\left( \frac{3}{5} \right)^6:\left( \frac{3}{5} \right)^4+ \frac{8}{5} -\left( \frac{3}{5} \right)^2\right] \cdot \frac{5}{8} =\left[\left( \frac{3}{5} \right)^{6-4}+ \frac{8}{5} -\left( \frac{3}{5} \right)^2\right]\cdot \frac{5}{8} =$
$\displaystyle =\left[\left( \frac{3}{5} \right)^2+ \frac{8}{5} -\left( \frac{3}{5} \right)^2\right] \cdot \frac{5}{8} = \frac{\not8}{\not5} \cdot \frac{\not5}{\not8} =\boxed{1}$