Задание 613

Решение:

• \({\largeа)}\ 5^{{-}1}+10^{{-}1}=\frac{1^{\backslash2}}{5\phantom{^{\backslash2}}}+\frac{1^{\backslash1}}{10\phantom{^{\backslash1}}}=\frac{2+1}{10}=\frac{3}{10}\)

• \({\largeб)}\ (0{,}5+1)^{{-}2}=\left(\frac{1}{2}+1\right)^{{-}2}=\left(1\frac{1}{2}\right)^{{-}2}=\left(\frac{3}{2}\right)^{{-}2}=\left(\frac{2}{3}\right)^2=\frac{4}{9}\)

• \({\largeв)}\ (2^{{-}4}+4^{{-}2})^{{-}1}=\left(\frac{1}{2^4}+\frac{1}{4^2}\right)^{{-}1}=\left(\frac{1}{16}+\frac{1}{16}\right)^{{-}1}=\left(\frac{2}{16}\right)^{{-}1}=\left(\frac{1}{8}\right)^{{-}1}=8\)

• \({\largeг)}\ (2-2^{{-}1})^{{-}1}=\left(2^{\backslash2}-\frac{1^{\backslash1}}{2\phantom{^{\backslash1}}}\right)^{{-}1}=\left(\frac{4-1}{2}\right)^{{-}1}=\left(\frac{3}{2}\right)^{{-}1}=\frac{2}{3}\)

• \({\largeд)}\ 3^{{-}1}+9^{{-}1}=\frac{1^{\backslash3}}{3\phantom{^{\backslash3}}}+\frac{1^{\backslash1}}{9\phantom{^{\backslash1}}}=\frac{3+1}{9}=\frac{4}{9}\)

• \({\largeе)}\ (0{,}2+1)^{{-}1}=\left(\frac{1}{5}+1\right)^{{-}1}=\left(1\frac{1}{5}\right)^{{-}1}=\left(\frac{6}{5}\right)^{{-}1}=\frac{5}{6}\)

• \({\largeж)}\ (4^{{-}2}-4^{{-}3})^{{-}1}=\left(\frac{1}{4^2}-\frac{1}{4^3}\right)^{{-}1}=\left(\frac{1^{\backslash4}}{16\phantom{^{\backslash4}}}-\frac{1^{\backslash1}}{64\phantom{^{\backslash1}}}\right)^{{-}1}=\left(\frac{4-1}{64}\right)^{{-}1}=\left(\frac{3}{64}\right)^{{-}1}=\frac{64}{3}=21\frac{1}{3}\)

• \({\largeз)}\ (3-3^{{-1}})^{{-}2}=\left(3^{\backslash3}-\frac{1^{\backslash1}}{3\phantom{^{\backslash1}}}\right)^{{-}2}=\left(\frac{9-1}{3}\right)^{{-}2}=\left(\frac{8}{3}\right)^{{-}2}=\left(\frac{3}{8}\right)^2=\frac{9}{64}\)