Question

Упростите несложные выражения

Answer 1

$a)\ \left(\sqrt[4]{a^3}\right)^{-\frac{4}{3}}=\left(a^{\frac{3}{4}}\right)^{-\frac{4}{3}}=a^{\frac{3}{4}\cdot\left(-\frac{4}{3}\right)}=a^{-1}=\frac{1}{a};\\\\\\b)\ a^{\frac{3}{4}}\cdot\sqrt[8]{a^5}=a^{\frac{3}{4}}\cdot a^{\frac{5}{8}}=a^{\frac{3}{4}+\frac{5}{8}}=a^{\frac{6+5}{8}}=a^{\frac{11}{8}}=a^{1\frac{3}{8}};\\\\\\c)\ \left(x^{\frac{7}{2}}y^{\frac{1}{6}}\right):\left(x^{-\frac{11}{4}}y^{\frac{2}{3}}\right)=x^{\frac{7}{2}-\left(-\frac{11}{4}\right)}y^{\frac{1}{6}-\frac{2}{3}}=$

$=x^{\frac{7}{2}+\frac{11}{4}}y^{\frac{1}{6}-\frac{2}{3}}=x^{\frac{14+11}{4}}y^{\frac{1-4}{6}}=x^{\frac{25}{4}}y^{-\frac{3}{6}}=x^{6\frac{1}{4}}y^{-\frac{1}{2}}=x^{6,25}y^{-0,5}=\\\\=\frac{x^{6,25}}{y^{0,5}}.$