Question

(Cefet-MG) Simplificando a expressão$\sqrt{\frac{x^{\frac{3}{2} }}{\sqrt[3]{x^4} } }$ , na qual x ∈ R+*, obtém-se?
RESPOSTA: $\sqrt[12]{x}$

Answer 1

Resposta:

√[x^(3/2) /∛x^4]

=√[x^(3/2) /x^(4/3)]

=√x^(3/2-4/3)

=√x^(9/6-8/6)

=√x^(1/6)

=[x^(1/6)] ^(1/2)

=x^(1/6 *1/2)

=x^(1/12)

= $\sqrt[12]{x}$

Answer 2

√[x^(3/2) /∛x^4]

=√[x^(3/2) /x^(4/3)]

=√x^(9/6-8/6)

=√x^(1/6)

=[x^(1/6)] ^(1/2)

=x^(1/6 *1/2)

=x^(1/12)