Вычислите:
1)

100^{5} : 1000^{2}

;
2)

\frac{3^{10} * (3^{3})^{5}}{(3^{5})^{4} * 3}

;
3)

\frac{4^{3} * 16^{2}}{2^{12}}

;
4)

\frac{45^{10}}{5^{8} * 3^{19}}

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Алгебре 7 класс Мерзляк. Номер №237

100^{5} : 1000^{2} = (10^{2})^{5} : (10^{3})^{2} = 10^{2 * 5} : 10^{3 * 2} = 10^{10} : 10^{6} = 10^{10 - 6} = 10^{4} = 10000

\frac{3^{10} * (3^{3})^{5}}{(3^{5})^{4} * 3} = \frac{3^{10} * 3^{3 * 5}}{3^{5 * 4} * 3} = \frac{3^{10} * 3^{15}}{3^{20} * 3} = \frac{3^{10 + 15}}{3^{20 + 1}} = \frac{3^{25}}{3^{21}} = \frac{3^{4}}{1} = 81

\frac{4^{3} * 16^{2}}{2^{12}} = \frac{(2^{2})^{3} * (2^{4})^{2}}{2^{12}} = \frac{2^{2 * 3} * 2^{4 * 2}}{2^{12}} = \frac{2^{6} * 2^{8}}{2^{12}} = \frac{2^{6 + 8}}{2^{12}} = \frac{2^{14}}{2^{12}} = \frac{2^{2}}{1} = 4

\frac{45^{10}}{5^{8} * 3^{19}} = \frac{(5 * 9)^{10}}{5^{8} * 3^{19}} = \frac{5^{10} * 9^{10}}{5^{8} * 3^{19}} = \frac{5^{10} * (3^{2})^{10}}{5^{8} * 3^{19}} = \frac{5^{10} * 3^{2 * 10}}{5^{8} * 3^{19}} = \frac{5^{10} * 3^{20}}{5^{8} * 3^{19}} = 5^{2} * 3^{1} = 25 * 3 = 75

ГДЗ Алгебра 7 класс Мерзляк, Полонский, Якир