# In what cases the “rule” (a^b)^c=a^(bc) doesn't necessarily hold when a<0?

I just saw that someone said that $(a^b)^c = a^{(bc)}$ sometimes doesn't hold if $a<0$. Can someone explain why?

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Let $a=-5$, $b=2$, and $c=\frac{1}{2}$. If we use the convention that says $25^{1/2}=5$, we have a problem. And if we use the convention $25^{1/2}=\pm 5$ we have a problem.