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# A.12: Poderes

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A continuación,$$x$$ y$$y$$ son números reales arbitrarios, y$$q$$ es una constante arbitraria que es estrictamente mayor que cero.

• $$q^0=1$$
• $$q^{x+y}=q^xq^y\text{,}$$$$q^{x-y}=\frac{q^x}{q^y}$$
• $$q^{-x}=\frac{1}{q^x}$$
• $$\big(q^x\big)^y=q^{xy}$$
• $$\lim\limits_{x\rightarrow\infty}q^x=\infty\text{,}$$$$\lim\limits_{x\rightarrow-\infty}q^x=0$$si$$q \gt 1$$
• $$\lim\limits_{x\rightarrow\infty}q^x=0\text{,}$$$$\lim\limits_{x\rightarrow-\infty}q^x=\infty$$si$$0 \lt q \lt 1$$
• La gráfica de$$2^x$$ se da a continuación. La gráfica de$$q^x\text{,}$$ para cualquiera$$q \gt 1\text{,}$$ es similar.

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