1) 0,29⋅59; 2) 43⋅253; 3) (\frac{1}{4})88; 4) (0,8)4⋅(125)4; 5) (2\frac{1}{3})4⋅(\frac{3}{7})4; 6) (0,5)17⋅ 219. 7) (c8)3⋅(c3)8;

Решим данные примеры, применяя свойства степеней.

1) $$0.2^9 \cdot 5^9 = (0.2 \cdot 5)^9 = 1^9 = 1$$

2) $$4^3 \cdot 25^3 = (4 \cdot 25)^3 = 100^3 = (10^2)^3 = 10^6$$

3) $$\left(\frac{1}{4}\right)^8 \cdot 8^8 = \left(\frac{1}{4} \cdot 8\right)^8 = (2)^8 = 256$$

4) $$(0.8)^4 \cdot (125)^4 = (0.8 \cdot 125)^4 = (100)^4 = (10^2)^4 = 10^8$$

5) $$\left(2\frac{1}{3}\right)^4 \cdot \left(\frac{3}{7}\right)^4 = \left(\frac{7}{3}\right)^4 \cdot \left(\frac{3}{7}\right)^4 = \left(\frac{7}{3} \cdot \frac{3}{7}\right)^4 = 1^4 = 1$$

6) $$(0.5)^{17} \cdot 2^{19} = (0.5)^{17} \cdot 2^{17} \cdot 2^2 = (0.5 \cdot 2)^{17} \cdot 4 = 1^{17} \cdot 4 = 1 \cdot 4 = 4$$

7) $$(c^8)^3 \cdot (c^3)^8 = c^{8\cdot3} \cdot c^{3\cdot8} = c^{24} \cdot c^{24} = c^{24+24} = c^{48}$$

Ответ: 1; 10⁶; 256; 10⁸; 1; 4; c⁴⁸