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Here are the "Laws of Exponents" and the rules that our Exponent Calculator uses to calculate your answer. For illustration, we use b for bases, and n for exponents.

$b^{\mathrm{n}}$ means b multiplied by itself n times. For example, $3^4$ is 3 x 3 x 3 x 3 = 81. However, there are certain exceptions and rules that our Exponent Calculator follows. Here are those rules with examples:

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Rule 1: Powers of one.

$b^1=b$

$0^1=0$

$1^1=1$

${\mathrm{123}}^1=\mathrm{123}$

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Rule 2: Powers of zero

$1^0=1$

${\mathrm{123}}^0=1$

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Rule 3: Powers of minus one

$b^{-1}=\frac{1}{b}$

${\mathrm{123}}^{-1}=\frac{1}{\mathrm{123}}=\; 0.00813$

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Rule 4: Negative Exponents

$b^{\mathrm{-n}}=\frac{1}{b^{\mathrm{n}}}$

${\mathrm{12}}^{-3}=\frac{1}{{\mathrm{12}}^3}=\; 0.00058$

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Conflicting Laws
If the base is 0 and the exponent is 0, then Rule 1 and Rule 2 conflict.

According to Rule 1 the answer should be 0 and according to Rule 2 the answer should be 1.

You can't have it both ways. Therefore, we consider this problem "undefined".

$0^0=\mathrm{undefined}$

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Answer too long
If your answer is too large or too small to display on your screen, you will get "Answer too Long" as the answer using our Exponent Calculator.

Almost 0
If your answer is too large or too small to display on your screen, you will get "Answer too Long" as the answer using our Exponent Calculator.

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