71. Вычислить: 1) 10^(2+√7)/(2^(2+√7)·5^(1+√7)); 2) 6^(3+√5)/(2^(2+√5)·3^(1+√5)); 3) (25^(1+√2)−5^(2√2))·5^(−1−2√2); 4) (2^(2√3)−4^(√3−1))·2^(−2√3).

Question

Accepted Answer

\(\frac{10^{2+\sqrt7}}{2^{2+\sqrt7}·5^{1+\sqrt7}}=\frac{2^{2+\sqrt7}5^{2+\sqrt7}}{2^{2+\sqrt7}5^{1+\sqrt7}}=5\).
\(\frac{6^{3+\sqrt5}}{2^{2+\sqrt5}·3^{1+\sqrt5}}=\frac{2^{3+\sqrt5}3^{3+\sqrt5}}{2^{2+\sqrt5}3^{1+\sqrt5}}=2·3^2=18\).
\((25^{1+\sqrt2}-5^{2\sqrt2})·5^{-1-2\sqrt2}=(5^{2+2\sqrt2}-5^{2\sqrt2})·5^{-1-2\sqrt2}=0\).
\((2^{2\sqrt3}-4^{\sqrt3-1})·2^{-2\sqrt3}=(2^{2\sqrt3}-2^{2\sqrt3-2})·2^{-2\sqrt3}=1-\frac14=\frac34\).

Ответ: 1) 5; 2) 18; 3) 0; 4) \(\frac34\).