Exercício 4: Simplifique as seguintes expressões: a) a1/2 · a1/6 b) a3/4 / a1/3 c) (a3b)2/3 d) a3/2a1/2 e) a-1/2 · a-3/2 Respostas: a) a2/3 b) a5...

Para simplificar as expressões fornecidas: a) a^(1/2) * a^(1/6) = a^(1/2 + 1/6) = a^(3/6 + 1/6) = a^(4/6) = a^(2/3) b) a^(3/4) / a^(1/3) = a^(3/4 - 1/3) = a^(9/12 - 4/12) = a^(5/12) c) (a^3 * b)^(2/3) = (a^(3*2/3) * b^(1*2/3)) = (a^2 * b^(2/3)) = a^2 * b^(2/3) d) a^(3/2) * a^(1/2) = a^(3/2 + 1/2) = a^(4/2) = a^2 e) a^(-1/2) * a^(-3/2) = a^(-1/2 - 3/2) = a^(-4/2) = a^(-2) Portanto, as respostas corretas são: a) a^(2/3) b) a^(5/12) c) a^2 * b^(2/3) d) a^2 e) a^(-2)