Question

Помогите пожалуйста с третьем заданием

Answer 1

Ответ:

$\frac{ {5}^{16} \times {3}^{16} }{ {15}^{14} } = \frac{(5 \times 3) ^{16} }{ {15}^{14} } = \frac{ {15}^{16} }{ {15}^{14} } = {15}^{16 - 14} = {15}^{2} = 225$

$\frac{ {27}^{2} \times {9}^{4} }{ {81}^{2} } = \frac{ {( {3}^{3}) }^{2} \times {(3}^{2}) ^{4} }{ { {(3}^{4} )}^{2} } = \frac{ {3}^{6} \times {3}^{8} }{ {3}^{8} } = {3}^{6}$

${5}^{20} \div { {(5}^{2}) }^{5} \div {5}^{8} = {5}^{20} \div {5}^{10} \div {5}^{8} = {5}^{20 - 10 - 8} = {5}^{2} = 25$

$\frac{ {3}^{10} \times {7}^{10} }{ {21}^{8} } = \frac{ {(3 \times 7)}^{10} }{ {21}^{8} } = \frac{ {21}^{10} }{ {21}^{8} } = {21}^{10 - 8} = {21}^{2}$

$\frac{ {32}^{3} \times {8}^{2} }{ {16}^{5} } = \frac{( {2}^{5}) ^{3} {8}^{2} }{ {16}^{5} } = \frac{ {2}^{15} \times {8}^{2} }{ {16}^{5} } = \frac{ {2}^{2} \times {2}^{13} \times {8}^{2} }{ {16}^{5} } = \frac{ {(2 \times 8)}^{2} \times {2}^{13} }{ {16}^{5} } = \frac{ {16}^{4} \times {2}^{4} \times {2}^{9} }{ {16}^{4} \times {2}^{4} } = {2}^{9}$

${7}^{15} \div { {(7}^{5}) }^{2} \div {7}^{3} = {7}^{15} \div {7}^{10} \div {7}^{3} = {7}^{15 - 10 - 3} = {7}^{2} = 49$