How do you simplify #125^(2/3)#?

2 Answers
Tony B · Don't Memorise
Feb 20, 2016

#=color(blue)(25#

Explanation:

#125^(2/3#

#125 = 5 xx 5 xx 5#

#125 = 5 ^3#

#125^(2/3) = 5^(3 (2/3)#

...................................................................................
Consider just the indices:
#3xx2/3 = (cancel(3)^1xx2)/(cancel(3)^1) = 2#
..............................................................................

# = 5^2 #

#=color(blue)(25#

Barney V.
Apr 5, 2017

#color(red)25#

Explanation:

#125^(2/3)#

#:.=root3(125^2)#

#:.=root3(15625)#

#:.=root3(25*25*25)#

#:.color(red)(=root3(a) xx root3(a) xx root3(a)=a#

#:.color(red)(=25#

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