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Is there a rule for adding exponential terms of like bases when only one base is negative. In other words, can they still be considered like bases.

$(-6)^2 \cdot (6)^3$

Intuitively this seems true, and I can't come up with a counter-example, but I would like to know for sure.

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    $\begingroup$ You could rewrite this as $((-1)\cdot(6))^2\cdot(6)^3=(-1)^2\cdot(6)^2\cdot(6)^3$ $\endgroup$
    – Mufasa
    Sep 22, 2013 at 21:14

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It's true. We have $(a\cdot b)^n=a^n \cdot b^n$ for any real numbers $a,b \in \mathbb{R}$, including integers (Of course!). So, you can first use the fact that $(-6)^2=(-1\cdot 6)^2 = (-1)^2 \cdot (6)^2$ and get rid of $-1$ and then continue as before.

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