How do you evaluate and simplify #(-243)^(1/5)#?

Answer 1

-3

Since the root (denominator) is 5, and since 5 is odd, the "-" sign extracts from the radical. #(-243)^(1/5)# = #-(243)^(1/5)# Since #3^5 = 243#, #-(243)^(1/5) = -(3^5)^(1/5)# #= -(3)^(5/5)# #= -(3)^1# #=-3#

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Answer 2

Eva Adamson

To evaluate and simplify (-243)^(1/5), first, find the principal fifth root of -243. The principal fifth root of a number is the real number that, when raised to the power of 5, equals the original number. In this case, (-3) is the principal fifth root of -243. Therefore, (-243)^(1/5) simplifies to -3.

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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.