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\(\Large a^x \cdot a^y = a^{x+y}\)

\(\,\)

\(\Large \dfrac{a^x}{a^y} = a^{x-y}\)

\(\,\)

\(\Large a^{-x} = \dfrac{1}{a^x}\)

\(\,\)

\(\Large (a^x)^y = a^{x \cdot y}\)

\(\,\)

\(\Large a^{\frac{x}{y}} = \sqrt[y]{a^x}\)

\(\,\)

\(\Large \sqrt[n]{a \cdot b} = \sqrt[n]{a} \cdot \sqrt[n]{b}\)

\(\,\)

\(\Large \sqrt[n]{\dfrac{a}{b}} = \dfrac{\sqrt[n]{a}}{\sqrt[n]{b}}\)

\(\,\)

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Markdown / Latex:

$$
a^x \cdot a^y = a^{x+y}
$$

$$
\dfrac{a^x}{a^y} = a^{x-y}
$$

$$
a^{-x} = \dfrac{1}{a^x}
$$

$$
(a^x)^y = a^{x \cdot y}
$$

$$
a^{\frac{x}{y}} = \sqrt[y]{a^x}
$$

$$
\sqrt[n]{a \cdot b} = \sqrt[n]{a} \cdot \sqrt[n]{b}
$$

$$
\sqrt[n]{\dfrac{a}{b}} = \dfrac{\sqrt[n]{a}}{\sqrt[n]{b}}
$$