275. Вычислить: 4) \((5^4\cdot10^{-4})^{0,25}+\left(\frac14\right)^{-1}-(5^3+3^{-2})^0+\left(5^{-0,8}\cdot5^{0,5}\cdot25^{\frac25}\right)^2\);

Question

275. Вычислить: 4) \((5^4\cdot10^{-4})^{0,25}+\left(\frac14\right)^{-1}-(5^3+3^{-2})^0+\left(5^{-0,8}\cdot5^{0,5}\cdot25^{\frac25}\right)^2\);

Accepted Answer

\((5^4\cdot10^{-4})^{0,25}=\left(\left(\frac5{10}\right)^4\right)^{\frac14}=\frac12\).

\(\left(\frac14\right)^{-1}=4\).

\((5^3+3^{-2})^0=1\).

Поскольку \(25^{\frac25}=5^{\frac45}\), получаем:
\(\left(5^{-0,8}\cdot5^{0,5}\cdot25^{\frac25}\right)^2=\left(5^{-\frac45+\frac12+\frac45}\right)^2=(5^{\frac12})^2=5\).

\(\frac12+4-1+5=\frac{17}{2}\).

Ответ: \(\frac{17}{2}=8,5\).