Question

calcule as potências em IR quando definidas:

c) $( { \frac{1}{2} })^{ \frac{1}{2} }$

d) $({ \sqrt{3} })^{ \frac{4}{5} }$

g) ${2}^{ \frac{4}{3} }$

h) ${8}^{0.666...}$

i) ${7}^{0.4}$
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Answer 1

c)

${ (\frac{1}{2} )}^{ \frac{1}{2} } = \sqrt{ \frac{1}{2} } = \frac{ \sqrt{1} }{ \sqrt{2} } = \frac{ \sqrt{2} }{2}$

d)

${( \sqrt{3}) }^{ \frac{4}{5} } = \sqrt[5]{ {3}^{4} } = \sqrt[5]{81}$

g)

${2}^{ \frac{4}{3} } = \sqrt[3]{ {2}^{4} } = \sqrt[3]{ {2}^{3}.2} \\ 2 \sqrt[3]{2}$

h)

${8}^{ 0,666} = {8}^{ \frac{6 \div 3}{9 \div 3 } } = {8}^{ \frac{2}{3} } \\ { ({2}^{3}) }^{ \frac{2}{3} } = {2}^{2} = 4$

i)

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