Question

срочно, с решением пж

Answer 1

Ответ:

1.

а)

$\sqrt[5]{ \frac{8 {a}^{3} }{ {b}^{2} } } \times \sqrt[5]{ \frac{4 {a}^{7} }{ {b}^{3} } } = \sqrt[5]{ \frac{8 {a}^{3} \times 4 {a}^{7} }{ {b}^{2} \times {b}^{3} } } = \\ = \sqrt[5]{ \frac{ {2}^{5} \times {a}^{5} \times {a}^{5} }{ {b}^{5} } } = \frac{2 \times a \times a}{b} = \frac{2 {a}^{2} }{b}$

б)

$\sqrt[4]{ \frac{8 {x}^{2} {y}^{5} \times 4 {x}^{3} y }{2x {y}^{2} } } = \sqrt[4]{ \frac{16 {x}^{5} {y}^{6} }{x {y}^{2} } } = \\ = \sqrt[4]{ \frac{ {2}^{4} {x}^{4} {y}^{4} }{1} } = 2xy$

в)

$\sqrt[6]{x \sqrt[3]{x \sqrt[5]{ {x}^{2} } } } = \sqrt[6]{x \sqrt[3]{x \times {x}^{ \frac{2}{5} } } } = \\ \sqrt[6]{x \sqrt[3]{ {x}^{ \frac{7}{5} } } } = \sqrt[6]{x \times {x}^{ \frac{7}{15} } } = \sqrt[6]{ {x}^{ \frac{22}{15} } } = \\ = {x}^{ \frac{22 }{15 \times 6} } = {x}^{ \frac{11} {45 } } = \sqrt[45]{ {x}^{11} }$

2.

а)

$\sqrt[3]{4096} = \sqrt[3]{ {64}^{2} } = \sqrt[3]{ ({4}^{3} )^{2} } = \\ = \sqrt[3]{ {(4 ^{2} )}^{3} } = {4}^{2} = 16$