Вычисли выражения со степенями a) 2^6 * 5^6 : 10^5

Решим примеры на степени: a) $2^6 \cdot 5^6 : 10^5 = (2\cdot5)^6 : 10^5 = 10^6 : 10^5 = 10^{6-5} = 10^1 = 10$ b) $(15^2)^5 : (3^9 \cdot 5^8) = 15^{2\cdot5} : (3^9 \cdot 5^8) = 15^{10} : (3^9 \cdot 5^8) = (3\cdot5)^{10} : (3^9 \cdot 5^8) = 3^{10} \cdot 5^{10} : 3^9 : 5^8 = 3^{10-9} \cdot 5^{10-8} = 3^1 \cdot 5^2 = 3 \cdot 25 = 75$ c) $(25 \cdot 4)^{10} : (2^{19} \cdot 5^{19}) = (25\cdot4)^{10} : (2\cdot5)^{19} = 100^{10} : 10^{19} = (10^2)^{10} : 10^{19} = 10^{20} : 10^{19} = 10^{20-19} = 10^1 = 10$ d) $(7^2)^5 : 49^3 \cdot 5^0 = 7^{2\cdot5} : (7^2)^3 \cdot 1 = 7^{10} : 7^{2\cdot3} = 7^{10} : 7^6 = 7^{10-6} = 7^4 = 7\cdot7\cdot7\cdot7 = 49\cdot49 = 2401$ e) $225 \cdot 15^5 \cdot 0^{12} = 225 \cdot 15^5 \cdot 0 = 0$ f) $\frac{1200 \cdot (5 \cdot 6)^5}{30^3} = \frac{1200 \cdot 30^5}{30^3} = 1200 \cdot 30^{5-3} = 1200 \cdot 30^2 = 1200 \cdot 900 = 1080000$ g) $\frac{4^{12} \cdot 8^8}{16^{10}} = \frac{(2^2)^{12} \cdot (2^3)^8}{(2^4)^{10}} = \frac{2^{24} \cdot 2^{24}}{2^{40}} = \frac{2^{24+24}}{2^{40}} = \frac{2^{48}}{2^{40}} = 2^{48-40} = 2^8 = 256$ h) $\frac{9^5 \cdot 27^4}{3^{20}} = \frac{(3^2)^5 \cdot (3^3)^4}{3^{20}} = \frac{3^{10} \cdot 3^{12}}{3^{20}} = \frac{3^{10+12}}{3^{20}} = \frac{3^{22}}{3^{20}} = 3^{22-20} = 3^2 = 9$ i) $\frac{5^5 \cdot 25^{10}}{125^7} = \frac{5^5 \cdot (5^2)^{10}}{(5^3)^7} = \frac{5^5 \cdot 5^{20}}{5^{21}} = \frac{5^{5+20}}{5^{21}} = \frac{5^{25}}{5^{21}} = 5^{25-21} = 5^4 = 625$