Laws of Exponents

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

${b}^{n}$ 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:

Rule 1: Powers of one.

${b}^{1}=b$

${0}^{1}=0$

${1}^{1}=1$

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

Rule 2: Powers of zero

${1}^{0}=1$

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

Rule 3: Powers of minus one

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

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

Rule 4: Negative Exponents

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

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

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".

${0}^{0}=\mathrm{undefined}$

Almost 0