Question

AYUUUUUDA PORFASS! se Los agradeceria​

Answer 1

En todos lo problemas hay usar teoria de exponentes

a)

$= \sqrt[5]{5 {}^{25} } \\ = {5 }^{ \frac{25}{5} } \\ = {5}^{5}$

b)

$= \sqrt[12]{ {z}^{18} {y}^{16} } \\ = {z}^{ \frac{18}{12} } {y}^{ \frac{16}{12} } \\ = {z}^{ \frac{3}{2} } {y}^{ \frac{4}{3} } \\ = \sqrt{ {z}^{3} } \times \sqrt[3]{ {y}^{4} }$

c)

$= \sqrt[3]{48} \\ = \sqrt[3]{ {2}^{3} \times 6} \\ = 2 \sqrt[3]{6}$

d)

$= \sqrt{50a {}^{2}b {}^{5} } \\ = 5a \sqrt{2 \times b {}^{5} }$

e)

$= \sqrt[8]{ {3}^{4} {y}^{24} {z}^{32} } \\ = \sqrt{3} \times {y}^{3} \times {z}^{4}$

f)

$= \sqrt[3]{81 {x}^{3} {y}^{4} } \\ = x \sqrt[3]{ {3}^{3} \times 3 \times {y}^{4} } \\ = 3x \sqrt[3]{3 {y}^{4} }$

g)

$= \sqrt[15]{ {2}^{5} {x}^{10} } \\ = \sqrt[3]{2} \times \sqrt[3]{ {x}^{2} } \\ = \sqrt[3]{2x {}^{2} }$

h)

$= \sqrt[5]{ \frac{ {a}^{13} }{24x {}^{2} } } \\ = \sqrt[5]{ \frac{a {}^{10} \times {a}^{3} }{24x {}^{2} } } \\ = {a}^{2} \times \sqrt[5]{ \frac{a {}^{3} }{24x {}^{2} } }$

i)

$= \sqrt{ \frac{27 {a}^{6} m {}^{3} {n}^{2} }{392 {b}^{9} {c}^{2} } } \\ = \sqrt{ \frac{9 \times 3 \times a {}^{6} \times m {}^{3} \times n {}^{2} }{49 \times 4 \times 2 \times b {}^{9} \times {c}^{2} } } \\ = \frac{3 {a}^{3} n}{7 \times 2 \times c} \times \sqrt{ \frac{3 {m}^{3} }{2 {b}^{9} } } \\ = \frac{3 {a}^{3} n}{14c} \sqrt{ \frac{3m {}^{3} }{2b {}^{9} } }$

j)

$= \sqrt[6]{ \frac{ {a}^{19} {b}^{174} }{ {c}^{32}d {}^{167} 256 } } \\ = \sqrt[6]{ \frac{ {a}^{18} \times a \times {b}^{29 \times 6} }{ {c}^{30} \times {c}^{2} \times {d}^{162} \times {d}^{5} \times {2}^{6} \times {2}^{2} } } \\ = \frac{a {}^{3} {b}^{29} }{ {2c}^{5} {d}^{27} } \times \sqrt[3]{ \frac{1}{2c} } \times \sqrt[6]{ \frac{a}{ {d}^{5} } }$