Question

степень с рациональным показателем​

Answer 1

1)

${a}^{ \frac{1}{3} } \times \sqrt{a} = {a}^{ \frac{1}{3} } \times {a}^{ \frac{1}{2} } = {a}^{ \frac{5}{6} }$

2)

${b}^{ \frac{1}{2} } \times {b}^{ \frac{1}{3} } \times \sqrt[6]{b} = {b}^{ \frac{1}{2} } \times {b}^{ \frac{1}{3} } \times {b}^{ \frac{1}{6} } = {b}^{1} = b$

3)

$\sqrt[3]{b} \div {b}^{ \frac{1}{6} } = {b}^{ \frac{1}{3} } \div {b}^{ \frac{1}{6} } = {b}^{ \frac{1}{6} }$

4)

${a}^{ \frac{4}{3} } \div \sqrt[3]{a} = {a}^{ \frac{4}{3} } \div {a}^{ \frac{1}{3} } = {a}^{1} = a$

5)

${x}^{1.7} \times {x}^{2.8} \div \sqrt{ {x}^{5} } = {x}^{1.7} \times {x}^{2.8} \div {x}^{ \frac{5}{2} } = {x}^{ \frac{17}{10} } \times {x}^{ \frac{14}{5} } \div {x}^{ \frac{5}{2} } = {x}^{ \frac{9}{2} } \div {x}^{ \frac{5}{2} } = {x}^{2}$

6)

${y}^{ - 3.8} \div {y}^{ - 2.3} \times \sqrt{ {y}^{3} } = {y}^{ - 1.5} \times {y}^{ \frac{3}{2} } = {y}^{ - \frac{ 3}{2} } \times {y}^{ \frac{3}{2} } = {y}^{0} = 1$