Question

Solve 27 to the power of (2/3)

Answer 1

`27^(2/3)=(3^3)^(2/3)=3^2=9`

Answer 2

9

Explanation:

`27^{(2)/(3)}\\\mathrm{Factor\:the\:number:\:}\:27=3^3\\=\left(3^3\right)^{(2)/(3)}\\\mathrm{Apply\:exponent\:rule}:\\\\\quad \left(a^b\right)^c=a^(bc),\:\quad \:a\ge 0\\\\\left(3^3\right)^{(2)/(3)}=3^(3)* (2)/(3)}\\\\3\=times (2)/(3)=2\\\\=3^2 \\\\=9`