SOLUTION: find the following 18 as the index square root of (-8)^18

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Question 398498: find the following 18 as the index square root of (-8)^18
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
root%2818%2C+%28-8%29%5E18%29
This is called "the 18th root of %28-8%29%5E18". The phrase "square root" has nothing to do with this expression.

The 18th root of "something" is whatever expression you can raise to the 18th power to get that "something". So root%2818%2C+%28-8%29%5E18%29 is whatever expression you can raise to the 18th power to get %28-8%29%5E18. The temptation would be to think that -8 to the 18th power results in %28-8%29%5E18. But even-numbered roots, like 18th roots, are supposed to be positive. The simplified answer is just 8!. (If you think about it it should become clear that %28-8%29%5E18 and %288%29%5E18 will both work out to the the same (very large) number. So
root%2818%2C+%28-8%29%5E18%29+=+8