Question

27 elevado a 0.333 ayudaaaaaaaaaaaaaaaaa

Answer 1

Explicación paso a paso:

< var > 0,333... = \frac{3}{9} < /var ><var>0,333...=93</var>

 

< var > 27^{0,333...} = 27^{\frac{3}{9}} < /var ><var>270,333...=2793</var>

 

27 | 3

9   | 3

3   | 3

1

 

27 = 3² * 3 = 3³

 

< var > 27^{\frac{3}{9}} = (3^{3})^{\frac{3}{9}} < /var ><var>2793=(33)93</var>

 

< var > (3^{3})^{\frac{3}{9}} = 3^{\frac{9}{9}} = 3^{1} = \boxed{3} < /var ><var>(33)93=399=31=3</var>

 

 

Answer 2

Escribamos la ecuación

$27^{0.333...} =x$

La fracción generatriz de 0,3333 es $\frac{1}{3}$, entonces

$27^{0.333...} =27^\frac{1}{3} =x$

Vamos a descomponer 27 en factores primos

$27^{\frac{1}{3} }=(3^{3})^{\frac{1}{3} }=x$

Apliquemos propiedades de las potencias,

$(a^{p})^{q} =a^{p q} \longrightarrow (3^{3})^{\frac{1}{3} }=(3^{3\frac{1}{3} })=3^{1} =\boxed{3=x}$