Question

Срочно! Дробная степень, задание на фото внутри!

Answer 1

$\frac{ {2}^{ \frac{1}{2} } \times 4 ^{ \frac{5}{4} } }{ {9}^{ \frac{2}{3} } \times {3}^{ \frac{2}{3} } } = \frac{ {2 \frac{1}{2} } \times {2}^{ \frac{5}{2} } }{ {27}^{ \frac{2}{3} } } = \frac{ {2}^{ \frac{6}{2} } }{ {(3}^{3} ) ^{ \frac{2}{3} } } = \frac{ {2}^{3} }{ {3}^{2} } = \frac{8}{9}$
действия отдельно:

${4}^{ \frac{5}{4} } = {(2}^{2} ) ^{ \frac{5}{4} } = {2}^{ \frac{2 \times 5}{4} } = {2}^{ \frac{5}{2} }$
${2}^{ \frac{1}{2} } \times {2}^{ \frac{5}{2} } = {2}^{ \frac{1 + 5}{2} } = {2}^{ \frac{6}{2} } = {2}^{3}$
${9}^{ \frac{2}{3} } \times {3}^{ \frac{2}{3} } = {(9 \times 3)}^{ \frac{2}{3} } = {27}^{ \frac{2}{3} }$

Answer 2

$\frac{2^{\frac{1}{2}}\, \cdot \, 4^{\frac{5}{4}}}{9^{\frac{2}{3}}\, \cdot \, 3^{\frac{2}{3}}}=\frac{2^{\frac{1}{2}}\, \cdot \, 2^{\frac{5}{2}}}{3^{\frac{4}{3}}\, \cdot \, 3^{\frac{2}{3}}}=\frac{2^{3}}{3^2}=\frac{8}{9}$