Question

Pesquise como transformar as situações abaixo em potencia com expoente fracionario


a) √4 elevado a 5° potencia


b) √7 elevado a 3° potencia


c) 4√5 elevado a 2° potencia


d) 3√6 elevado a 4° potencia


e) √10


f) 3√2 elevado a 5° potencia


a g) eu já fiz


h) √0,36

Answer 1

Resposta:

$a) (\sqrt{4} )^{5}=(\sqrt{4} )^{5}=(\sqrt{2^{2}} )^{5}=(2^{\frac{2}{2}})^5=(2^{1}) ^5=2^{5}=2^{\frac{5}{1}}\\\\b)(\sqrt{7})^{3}=(7^{\frac{1}{2} })^{3}=7^{\frac{3}{2}}\\\\c)(4\sqrt{5} )^{2}=(2^{2}5^{\frac{1}{2} } )^{2}=2^{2.2}5^{\frac{2}{2} }=x^{4} .5^{1} =x^{\frac{4}{1}} .5^{\frac{1}{1} }\\\\d)(3\sqrt{6} )^{4}=(3.(2.3)^{\frac{1}{2} } )^{4}=(2^{\frac{1}{2} }.3^{(1+\frac{1}{2})} )^{4}=(2^{\frac{1}{2} }.3^{\frac{3}{2}})^{4}=2^{\frac{4}{2} }.3^{\frac{12}{2}}=2^{\frac{2}{1} }.3^{\frac{6}{1}}$

$e)\sqrt{10}=(2.5)^{\frac{1}{2}}=2^{\frac{1}{2} }.5^{\frac{1}{2} }\\\\f) (3\sqrt{2} )^{5}=3^{\frac{5}{1} }.2^{\frac{5}{2} }\\\\h)\sqrt{0,36} =\sqrt{\frac{36}{100} } =\sqrt{\frac{9}{25}} =\sqrt{\frac{3^{2}}{5^{2}}} =(\frac{3^{2}}{5^{2}} })^{\frac{1}{2}} =\frac{3}{5} =3.5^{-1}=3^{\frac{1}{1} }.5^{\frac{-1}{1} }$

Propriedades:

$(a^{m})^{n}=a^{m.n}\\\\\sqrt[n]{x^m} =x^{\frac{m}{n} }\\\\a^{m}a^{n}=a^{m+n}$