Question

Решите уравнения 9 шт. [БЕЗ ОДЗ]

Answer 1

$1) \: {4}^{0.76} \times {8}^{0.16} = {2}^{1.52} \times {2}^{0.48} = {2}^{1.52 + 0.48} = {2}^{2} = 4$
$2) \: \frac{ {2}^{3.2} }{ {4}^{1.6} } = {2}^{3.2 - 3.2} = 1$
${4}^{ \frac{3}{7} } \times {16}^{ \frac{2}{7} } = {2}^{ \frac{6}{7} } \times {2}^{ \frac{8}{7} } = {2}^{ \frac{6}{7} + \frac{8}{7} } = {2}^{2} = 4$
$4) \: \frac{ {3}^{4.5} \times {4}^{4.5} }{ {12}^{3.5} } = \frac{ {3}^{4.5} \times {4}^{4.5} }{ {3}^{3.5} \times {4}^{3.5} } = {3}^{4.5 - 3.5} \times {4}^{4.5 - 3.5} = 3 \times 4 = 12$
$5) \: {6}^{2.3} \times {3}^{ - 0.3} \div {2}^{2.3} ={2}^{2.3} \times {3}^{2.3} \times {3}^{ - 0.3} \div {2}^{2.3} = {2}^{2.3 - 2.3} \times {3}^{2.3 - 0.3} = {2}^{0} \times {3}^{2} = 9$
$6) \: ( \frac{ {10}^{ \frac{1}{3} } \times {10}^{ \frac{1}{4} } }{ \sqrt[12]{10} } )^{2} = ({10}^{ \frac{1}{3} + \frac{1}{4} - \frac{1}{12} } )^{2} = ( {10}^{ \frac{6}{12} } )^{2} = 10$
$7) \: \frac{( {7}^{ \frac{3}{5} } \times {9}^{ \frac{2}{3} } )^{15} }{ {63}^{9} } = \frac{ {7}^{9} \times {9}^{10} }{ {7}^{9} \times {9}^{9} } = {7}^{9 - 9} \times {9}^{10 - 9} = 9$
$8) \: {2.5}^{ \frac{1}{5} } \times {2}^{ \frac{2}{5} } \times {10}^{ \frac{4}{3} } = ( \frac{5}{2} )^{ \frac{1}{5} } \times {2}^{ \frac{2}{5} } \times {2}^{ \frac{4}{3} } \times {5}^{ \frac{4}{3} } = {5}^{ \frac{1}{5} + \frac{4}{3} } \times {2}^{ \frac{2}{5} + \frac{4}{3} - \frac{1}{5} } = {5}^{ \frac{23}{15} } \times {2}^{ \frac{23}{15} } = {10}^{ \frac{23}{15} }$
$\frac{ {36}^{5.3} }{ {6}^{8.6} } = {6}^{10.6 - 8.6} = {6}^{2} = 36$