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)

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