SOLUTION: What positive number is 3 times its cube root?

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Question 572920: What positive number is 3 times its cube root?
Answer by TutorDelphia(193) About Me  (Show Source):
You can put this solution on YOUR website!
You need to be pretty good with exponents to do this problem.
First let's write the problem in equation form:
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n=3n%5E%281%2F3%29
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Divide both sides by n%5E%281%2F3%29
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n%5E1%2Fn%5E%281%2F3%29=3
use the exponent power rule to 1-1/3=2/3
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n%5E%282%2F3%29=3
Take both sides to the 3/2 power
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n=3%5E%283%2F2%29
simplify this:
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n=sqrt%2827%29
And to check, 3%2A%2827%5E%281%2F2%29%29%5E%281%2F3%29 =~5.196 and sqrt%2827%29=~5.196
because both equal 3%2Asqrt%283%29