Question

E5. B și C vă rog frumos

Answer 1

$E5. A. b) 81^{-\frac{3}{4}}*27^{-\frac{2}{3}}*(\frac{1}{0,(3)})^{5}=\\ =(3^{4})^{-\frac{3}{4}}*(3^{3})^{-\frac{2}{3}}*(\frac{1}{\frac{1}{3}})^{5}=\\ =3^{4*(-\frac{3}{4})}*3^{3*(-\frac{2}{3})}*(1*\frac{3}{1})^{5}=\\ =3^{-3}*3^{-2}*3^{5}=\\ =(\frac{1}{3})^{3}*(\frac{1}{3})^{2}*3^{5}=\\ =\frac{1}{3^{3}}*\frac{1}{3^{2}}*3^{5}=\\ =\frac{1}{3^{5}}*3^{5}=1.$

$c)3^{\frac{4}{3}}*9^{2}*(27)^{-\frac{5}{6}}*3^{-\frac{3}{2}}=\\ =3^{\frac{4}{3}}*(3^{2})^{2}*(3^{3})^{-\frac{5}{6}}*3^{-\frac{3}{2}}=\\ =3^{\frac{4}{3}}*3^{4}*3^{-\frac{5}{2}}*3^{-\frac{3}{2}}=\\ =3^{\frac{4}{3}+4-\frac{5}{2}-\frac{3}{2}}=\\ =3^{\frac{8+24-15-9}{6}}=\\ =3^{\frac{8}{6}}=3^{\frac{4}{3}}=\sqrt[3]{3^{4}}=3\sqrt[3]{3}.$

/rfd