Question

calcule as potencias em |R quando definidas:
A) 5^ 2/7
B) 2^ 3/7
C) ( 1/2 )^ 1/2
D) ( raiz de 3 )^ 4/5
E) 9^ 1/2
F) 0^ 1/8
G) 2^ 4/3
H) 8^ 0,666
I) 7^ 0,4

Answer 1

A)5^{ \frac{2}{7} } = \sqrt[7]{5^2} = \sqrt[7]{25} =1,58382
 B) 2^{ \frac{3}{7} } = \sqrt[7]{2^3} = \sqrt[7]{8} =1,3459
 C) \frac{1}{2} ^{ \frac{1}{2} } = \frac{ 1^{ \frac{1}{2} } }{ 2^{ \frac{1}{2} } } = \frac{1}{ \sqrt{2} } = \frac{ \sqrt{2} }{2} [/tex]
D)( \sqrt{3}) ^{ \frac{4}{5} } =( 3^{ \frac{1}{2} } )^ \frac{4}{5} = 3^{ \frac{4}{10} } = 3^{ \frac{2}{5} } = \sqrt[5]{3^2} = \sqrt[5]{9} =1,55185
 E) 9^{ \frac{1}{2} } = \sqrt{9} =+_{-} 3
 F) 0^{ \frac{1}{8} } =0 \\ \\
G) 2^{ \frac{4}{3} } = \sqrt[3]{2^4} = \sqrt[3]{2^3.2} =2 \sqrt[3]{2} =2,51984 \\ \\ H) 8^{0,666} = 8^{ \frac{666}{1000} } = 8^{ \frac{333}{500} } = \sqrt[500]{ 8^{333} } = \sqrt[500]{ (2^{ 3)^{333} } } = \sqrt[500]{ 2^{999} } = [/tex]
$= \sqrt[500]{ 2^{500} . 2^{499} } =2 \sqrt[500]{ 2^{499} } =3,99$

$I) 7^{0,4} = 7^{ \frac{4}{10} } =7^{ \frac{2}{5} } = \sqrt[5]{7^2} = \sqrt[5]{49} =2,17791$