Решение:

1. $$\left(4 \frac{3}{3}\right)^2 = (4 + 1)^2 = 5^2 = 25$$ $$\textbf{Ответ: 25}$$
2. $$\left(6 : \frac{2}{3}\right)^3 = \left(6 \cdot \frac{3}{2}\right)^3 = \left(\frac{6 \cdot 3}{2}\right)^3 = \left(\frac{18}{2}\right)^3 = 9^3 = 729$$ $$\textbf{Ответ: 729}$$
3. $$7 + 7^2 = 7 + 49 = 56$$ $$\textbf{Ответ: 56}$$
4. $$(4.9 - 5.1)^5 = (-0.2)^5 = -0.00032$$ $$\textbf{Ответ: -0.00032}$$
5. $$6^3 - (-8)^2 = 216 - 64 = 152$$ $$\textbf{Ответ: 152}$$
6. $$-10^4 + (-5)^3 = -10000 + (-125) = -10000 - 125 = -10125$$ $$\textbf{Ответ: -10125}$$
7. $$(-1)^5 - (-1)^{10} = -1 - 1 = -2$$ $$\textbf{Ответ: -2}$$