Question

escreva na forma de unica potencia de 3


$a) (3^{\frac{1}{3} })^{\frac{1}{2} } \\\\b) 3^{\frac{2}{3} } : 3^{\frac{1}{6} } \\\\c) 27^{\frac{1}{6} }$

Answer 1

Explicação passo-a-passo:

Lembre-se que:

$(a^m)^n=a^{m\cdot n}$

$a^{m}\div a^{n}=a^{m-n}$

a) $(3^{\frac{1}{3}})^{\frac{1}{2}}=3^{\frac{1}{3}\cdot\frac{1}{2}}=3^{\frac{1}{6}}$

b) $3^{\frac{2}{3}}\div3^{\frac{1}{6}}=3^{\frac{2}{3}-\frac{1}{6}}=3^{\frac{4-1}{6}}=3^{\frac{3}{6}}=3^{\frac{1}{2}}$

c) $27^{\frac{1}{6}}=(3^3)^{\frac{1}{6}}=3^{\frac{3}{6}}=3^{\frac{1}{2}}$