Understanding Properties of Exponents

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latex="a^{m+n}">

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latex="a^{m \cdot n}">

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latex="a^{m-n}">

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latex="\frac{1}{a^n}">

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latex="2^{3+4} = 2^7">

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latex="3^{2 \cdot 3} = 3^6">

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latex="5^{6-2} = 5^4">

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latex="1">

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latex="\frac{1}{4^2} = \frac{1}{16}">