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

1 Answer
Deltiv
Mar 22, 2018

#(125x)^(2/3)# = #(125^(2/3)*x^(2/3))# = #(5^(2)*x^(2/3))# = #(25*x^(2/3))#

Explanation:

#(125x)^(2/3)#
says:
( remember that #(125x)^(2/3)# = #((125x)^(2))^(1/3)# )
125x multiplied by itself twice(because of the 2 exponent) (i'll say that in math: (125x)^(2) ) then all that multiplied by itself 1/3 times (aka taking the cube root of that)
#(125x)^(2) = 15625*x^2#
now for cube root:
#(15625*x^2)^(1/3)#
#(15625^(2/3)*x^(2/3))#
#25*x^(2/3)#
you could've also instead of squaring first, then taking the cube root,
you could've of cube rooted first, then squared,
or:
you could've done both at the same time: (which is what you see in the awnser up top)

Related questions
See all questions in Fractional Exponents
Impact of this question
4036 views around the world
You can reuse this answer
Creative Commons License