Question

Alguien sabe esto? Ayuda

Answer 1

Respuesta:

a.

$\sqrt[3]{ \sqrt[4]{a} } = \sqrt[3 \times 4]{a} = \sqrt[12]{a} = {a}^{ \frac{1}{12} }$

b.

$\sqrt{ \sqrt[3]{ {x}^{2} \sqrt[5]{ {x}^{3} } } } = \sqrt[2]{ \sqrt[3]{ {x}^{2}. {x}^{ \frac{3}{5} }}} = \sqrt[2]{ \sqrt[3]{ {x}^{2 + \frac{3}{5} } } }$

$\sqrt[2]{ \sqrt[3]{ {x}^{ \frac{10}{5} + \frac{3}{5} } } } = \sqrt[2]{ \sqrt[3]{ {x}^{ \frac{10 + 3}{5} } } } = \sqrt[2]{ \sqrt[3]{ {x}^{ \frac{13}{5} } } }$

$\sqrt[2 \times 3]{{x}^{ \frac{13}{5} } } = \sqrt[6]{ {x}^{ \frac{13}{5} } } = {x}^{ \frac{13}{6 \times 5} } = {x}^{ \frac{13}{30} }$

c.

$\sqrt{n \sqrt[5]{n \sqrt[6]{n} } } = \sqrt[2]{n \sqrt[5]{n. {n}^{ \frac{1}{6} } } } = \sqrt[2]{n \sqrt[5]{ {n}^{1} . {n}^{ \frac{1}{6} } } } =$

$\sqrt[2]{n \sqrt[5]{ {n}^{1 + \frac{1}{6}} }}=\sqrt[2]{n \sqrt[5]{ {n}^{ \frac{6}{6} + \frac{1}{6}} }}=\sqrt[2]{n \sqrt[5]{ {n}^{\frac{6 + 1}{6}} }}=$

$\sqrt[2]{n \sqrt[5]{ {n}^{\frac{7}{6}} }}= \sqrt[2]{n. {n}^{ \frac{7}{5 \times 6} } } = \sqrt[2]{n. {n}^{ \frac{7}{30} } }$

$= \sqrt[2]{ {n}^{1} . {n}^{ \frac{7}{30} } } = \sqrt[2]{ {n}^{1 + \frac{7}{30} } } = \sqrt[2]{ {n}^{ \frac{30}{30} + \frac{7}{30} } } =$

$\sqrt[2]{ {n}^{ \frac{30 + 7}{30}}} = \sqrt[2]{ {n}^{ \frac{37}{30}}} = {n}^{ \frac{37}{2 \times 30} } = {n}^{ \frac{37}{60} }$