275. Вычислить: 3) \((15^0)^n+(81\cdot10^{-4})^{0,25}-\left(3^{-0,8}\cdot5^{0,5}\cdot81^{\frac15}\right)^{-2}+\left(\frac54\right)^{-2}\);

\((15^0)^n=1^n=1\).

\((81\cdot10^{-4})^{0,25}=\left(\frac{81}{10000}\right)^{\frac14}=\left(\frac3{10}\right)^4{}^{\frac14}=\frac3{10}\).

Так как \(3^{-0,8}=3^{-\frac45}\), \(81^{\frac15}=3^{\frac45}\), то
\(3^{-0,8}\cdot5^{0,5}\cdot81^{\frac15}=\sqrt5\).

Следовательно, \(-(\sqrt5)^{-2}=-\frac15\).

\(\left(\frac54\right)^{-2}=\left(\frac45\right)^2=\frac{16}{25}\).

\(1+\frac3{10}-\frac15+\frac{16}{25}=\frac{87}{50}\).

Ответ: \(\frac{87}{50}=1,74\).