Resposta:
Explicação passo a passo:
Regra:
[tex]a^{\frac{m}{n} } =\sqrt[n]{a^{m} }[/tex]
a)
[tex]43^{\frac{1}{9} } =\sqrt[9]{43}[/tex]
b)
[tex]7^{-\frac{2}{3} } =(7^{-1}) ^{\frac{2}{3} } =(\frac{1}{7}) ^{\frac{2}{3} } =\sqrt[3]{(\frac{1}{7} )^{2} } =\sqrt[3]{\frac{1}{49} }[/tex]
c)
[tex](\frac{1}{4}) ^{\frac{1}{4} } =\sqrt[4]{\frac{1}{4} } =\frac{\sqrt[4]{1} }{\sqrt[4]{4} } =\frac{1}{\sqrt[4]{2^{2} } } =\frac{1}{\sqrt{2} } =\frac{\sqrt{2} }{2}[/tex]
d)
[tex]0,25=1/4[/tex]
[tex](\frac{1}{4}) ^{\frac{5}{12} } =\sqrt[12]{(\frac{1}{4}) ^{5} } =\sqrt[12]{\frac{1}{4^{5} } } =\sqrt[12]{\frac{1}{1024} }[/tex]
