How to simplify the expression ${(- 8)}^{\frac{2}{8}}$ $(-8)^(2/8)$ ?

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Answer 1 · 2017-10-21T21:28:25

No real solution

First reduce the fraction in the exponent, so:

${(- 8)}^{\frac{2}{8}} = {(- 8)}^{\frac{1}{4}}$ $(-8)^(2/8)=(-8)^(1/4)$

Then let's use the definition of a radical:

$a^{\frac{b}{c}} = \sqrt[c]{a^{b}}$ $a^(b/c)=root(c)(a^b)$

So:

${(- 8)}^{\frac{1}{4}} = \sqrt[4]{- 8}$ $(-8)^(1/4)=root(4)(-8)$

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

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

How to simplify the expression (-8)^(2/8)(−8)28(-8)^(2/8) ?