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If #(x-1)^(2/3) =25# then x equals what?

Answer 1

#x=126#

This problem might appear scary because to isolate #x#, you need to so some tricky stuff with exponents.

But if you think about it, we can cancel out the #2/3# by raising each side to #3/2#, because when you raise an exponent to an exponent it serves to multiply the two, and #2/3*3/2=1#.

Based on this, we can raise #25# to the power of #3/2#, as well as #(x-1)^(2/3)# in order to get the equation

#(x-1)^(2/3*3/2)=25^(3/2)#
#(x-1)=125#
#x=126#

Sure enough, if you plug in 126 for #x#, you get #25# as your output:

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.