Question

How do you simplify `(27/8)^(2/3)`?

Answer 1

`= 9 /4`

Explanation:

`(27/8)^(2/3)`

• Simplifying `color(blue)(27`
  `27 = 3 *3 *3 = color(blue)(3 ^3`

• Simplifying `color(green)(8`
  `8 = 2 *2 *2 = color(green)(2 ^3`

The expression now becomes:
`(27/8)^(2/3) = (color(blue)(3^3 )/ color(green)(2^3))^(2/3)`

• Applying property:
  `color(blue)((a/b)^m = a^m/ b^m`

#= (color(blue)(3^3 )/ color(green)(2^3))^(2/3) = (3^(3 * (2/3)))/(2^ (3 * (2/3))#

`= (3^(cancel3 * (2/3)))/(2^(cancel3 * (2/3))`

`= 3^2 / 2 ^2`

`= 9 /4`