Question

Пж, с решением.
Даю 50 баллов

Answer 1

$1)a) {3}^{7} \times ( {3}^{2} )^{3} \div {3}^{10} = {3}^{7} \times {3}^{6} \div {3}^{10} = {3}^{3} = 3 \times 3 \times 3 = 27 \\ b) {5}^{20} \div ( {5}^{2} )^{5} \div {5}^{8} = {5}^{20} \div {5}^{10} \div {5}^{8} = {5}^{2} = 5 \times 5 = 25 \\ \\ 2)a) \frac{ {9}^{4} }{ {3}^{7} } = \frac{ {(3 \times 3)}^{4} }{ {3}^{7} } = \frac{ {3}^{8} }{ {3}^{7} } = 3 \\ \\ b) \frac{ {8}^{5} }{ {4}^{6} } = \frac{ {8}^{5} }{(4 \times 4)^{3} } = \frac{ {8}^{5} }{ {8}^{3} } = {8}^{2} = 8 \times 8 = 64 \\ \\ c) \frac{ {27}^{2} \times {9}^{4} }{ {81}^{2} } = \frac{(3 \times 3 \times 3)^{2} \times (3 \times 3)^{4} }{ ({3 \times 3 \times 3 \times 3})^{2} } = \frac{ {3}^{6} \times {3}^{8} }{ {3}^{8} } = {3}^{6} = 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 729 \\ \\ 3)a)\frac{ {10}^{12} }{ {2}^{6} \times {5}^{6} } = \frac{ {10}^{12} }{( {2 \times 5})^{6} } = \frac{ {10}^{12} }{ {10}^{6} } = {10}^{6} = 10 \times 10 \times 10 \times 10 \times 10 \times 10 = 1000000 \\ \\ b) \frac{ {5}^{16} \times {3}^{16} }{ {15}^{14} } = \frac{(5 \times 3)^{16} }{ {15}^{14} } = \frac{ {15}^{16} }{ {15}^{14} } = {15}^{2} = 225 \\ \\ c) \frac{ {12}^{6} }{ {3}^{5} \times {4}^{5} } = \frac{ {12}^{6} }{(3 \times 4)^{5} } = \frac{ {12}^{6} }{ {12}^{5} } = 12$