Question

Simplifique a seguinte potência de expoente racional:
a) 81^(-0,25)

b)16 elevado a 5/4 elevado a 2/5

Answer 1

$a) 81^{-0,25} = (3^4)^{-1/4} = 3^{-4/4} = 3^{-1} = 1/3$

$b) (16^{5/4})^{2/5} = 16^{10/20} = (2^4)^{1/2} = 2^{4/2} = 2^2 = 4$

Answer 2

a) 81^(-0,25)

(2^4)^(-1/4) ==> 2^-4/4 ==> 2^-1
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b)16 elevado a 5/4 elevado a 2/5

(16^5/4)^2/5 ==> ((2^4)^5/4)^2/5 ==> 2^40/20 ==> 2^2 ==> 4