Задание №5. Вычислите: а) \(2^5\cdot0,5^4\); б) \(4^9\cdot0,25^{10}\); г) \(\left(2\frac14\right)^{15}\cdot\left(\frac49\right)^{17}\); д) \((-1,2)^{25}\cdot\left(-\frac56\right)^{23}\).

1. \(2^5\cdot0.5^4=2^5\cdot\left(\frac12\right)^4=2^{5-4}=2\).
2. \(4^9\cdot0.25^{10}=2^{18}\cdot\left(\frac14\right)^{10}=2^{18-20}=\frac14\).
3. \(\left(2\frac14\right)^{15}\cdot\left(\frac49\right)^{17}=\left(\frac94\right)^{15}\cdot\left(\frac49\right)^{17}=\left(\frac49\right)^2=\frac{16}{81}\).
4. \((-1.2)^{25}\cdot\left(-\frac56\right)^{23}=\left(-\frac65\right)^{25}\cdot\left(-\frac56\right)^{23}=\frac{6^2}{5^2}=\frac{36}{25}=1.44\).

Ответ: а) 2; б) \(\frac14\); г) \(\frac{16}{81}\); д) \(\frac{36}{25}\).