How to simplify the expression #(-8)^(2/8)# ?

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Answer 1 · 2017-10-21T21:28:25

No real solution

First reduce the fraction in the exponent, so:

#(-8)^(2/8)=(-8)^(1/4)#

Then let's use the definition of a radical:

#a^(b/c)=root(c)(a^b)#

So:

#(-8)^(1/4)=root(4)(-8)#

Or in other words: what number times itself four times is #-8#?

Since no real number can multiply by itself an even amount of times to get a negative number, there is no real solution.