Question

Lets evaluate (3^6)^1/2

step by step.

Answer 1

`\displaystyle\bf \boldsymbol{\boxed{(a^n)^m=a^(n\cdot m)}} \\\\(3^6)^{(1)/(2)} =3^{(6)/(2) }=3^3=\boldsymbol{{\boxed {27}}}`

Answer 2

27

Explanation:

`\bigg(3^6\bigg)^{(1)/(2)}`

use

`(a^n)^m=a^(n\cdot m)`

`\bigg(3^6\bigg)^{(1)/(2)}=3^{6\cdot(1)/(2)`

simplify

`6\!\!\!\!\diagup^3\cdot(1)/(2\!\!\!\!\diagup_1)=3\cdot(1)/(1)=3\cdot1=3`

other

`6\cdot(1)/(2)=(6\cdot1)/(2)=(6)/(2)=3`

therefore

`\bigg(3^6\bigg)^{(1)/(2)}=3^{6\cdot(1)/(2)}=3^3=\underbrace{3\cdot3\cdot3}_(3)=27`