SOLUTION: I cannot figure out extraneous solutions in radical equations with fractional exponents. Ex: (2x)^3/4=8 My teacher sucks and won't help me in class & I am failing.

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Question 419206: I cannot figure out extraneous solutions in radical equations with fractional exponents.
Ex: (2x)^3/4=8

My teacher sucks and won't help me in class & I am failing.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

(2x)^3/4=8

+root%284%2C%282x%29%5E3%29+=+8+

%282x%29%5E3+=+8%5E4+     |Taking both sides of the equation to the 4th power

 8x^3 = 8^4    |8^4 = 8*8*8*8

  x^3 = 8^3

   x = 8



CHECKING our Answer***

 root%284%2C16%5E3%29+=+root%284%2C%282%2A2%2A2%2A2%29%5E3%29+=++2%5E3+=+8