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

1 Answer
Apr 29, 2016

Answer:

# = 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#