Question

[ (216) ^ 2/3 ] ^ 1/2​

Answer 1

Answer:

$\mathrm{Simplify}\:\left(\left(216\right)^{\dfrac{2}{3}}\right)^{\dfrac{1}{2}}:\quad 6$

Step-by-step explanation:

$\left(\left(216\right)^{\dfrac{2}{3}}\right)^{\dfrac{1}{2}}$

$\gray{\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}}$

$=216^{\dfrac{2}{3}\cdot \dfrac{1}{2}}$

$\gray{\mathrm{Cross-cancel:}\:2}$

$=216^{\dfrac{1}{3}}$

$\gray{\mathrm{Factor\:the\:number:\:}\:216=6^3}$

$=\left(6^3\right)^{\dfrac{1}{3}}$

$\gray{\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}}$

$\gray{\left(6^3\right)^{\dfrac{1}{3}}=6^{3\cdot \dfrac{1}{3}}=6}$

$=6$