57. Представьте выражение в виде степени и вычислите его значение: 1) 3⁴ ⋅ 3⁵; 2) 2⁵: 2²; 3) 5¹¹ ⋅ 5⁷ : 5¹⁵; 4) 29¹⁰ ⋅ 29⁶ : 29¹⁴; 5) (-2/3)²⁴ : (-2/3)²² ⋅ (-2/3)³; 6) 7¹³ ⋅ 7⁶ / 7¹⁷; 7) (0,4)¹² ⋅ (0,4)¹⁴ / (0,4)⁵ ⋅ (0,4)¹⁹; 8) 3³ ⋅ 27; 9) 128 ⋅ 2² : 2⁵; 10) 4⁴⁰ / 4⁵ ⋅ 64

1. $$3^4 \cdot 3^5 = 3^{4+5} = 3^9 = 19683$$.
2. $$2^5 : 2^2 = 2^{5-2} = 2^3 = 8$$.
3. $$5^{11} \cdot 5^7 : 5^{15} = 5^{11+7-15} = 5^{3} = 125$$.
4. $$29^{10} \cdot 29^6 : 29^{14} = 29^{10+6-14} = 29^{2} = 841$$.
5. $$\left(-\frac{2}{3}\right)^{24} : \left(-\frac{2}{3}\right)^{22} \cdot \left(-\frac{2}{3}\right)^{3} = \left(-\frac{2}{3}\right)^{24-22+3} = \left(-\frac{2}{3}\right)^{5} = -\frac{32}{243}$$.
6. $$\frac{7^{13} \cdot 7^6}{7^{17}} = \frac{7^{13+6}}{7^{17}} = \frac{7^{19}}{7^{17}} = 7^{19-17} = 7^{2} = 49$$.
7. $$\frac{(0,4)^{12} \cdot (0,4)^{14}}{(0,4)^5 \cdot (0,4)^{19}} = \frac{(0,4)^{12+14}}{(0,4)^{5+19}} = \frac{(0,4)^{26}}{(0,4)^{24}} = (0,4)^{26-24} = (0,4)^{2} = 0,16$$.
8. $$3^3 \cdot 27 = 3^3 \cdot 3^3 = 3^{3+3} = 3^6 = 729$$.
9. $$128 \cdot 2^2 : 2^5 = 2^7 \cdot 2^2 : 2^5 = 2^{7+2-5} = 2^{4} = 16$$.
10. $$\frac{4^{40}}{4^5 \cdot 64} = \frac{4^{40}}{4^5 \cdot 4^3} = \frac{4^{40}}{4^{5+3}} = \frac{4^{40}}{4^{8}} = 4^{40-8} = 4^{32} = 1.8446744 \times 10^{19}$$.

Ответ: 1) 19683; 2) 8; 3) 125; 4) 841; 5) -32/243; 6) 49; 7) 0,16; 8) 729; 9) 16; 10) 1.8446744 × 10¹⁹.