Exponents

The laws of exponents, unlike laws of motion, are in no particular order

1.am×an=am+n1.\;a^m \times a^n = a^{m+n}
2.aman=amn2. \; \frac{a^m}{a^n} = a^{m-n}
3.am×bm=(a×b)m3. \; a^m \times b^m = (a\times b)^m
4.anm=anm4.\; a^{\frac{n}{m}} = \sqrt[m]{a^n}
5.am=1am5. \; a^{-m} = \frac{1}{a^m}
6.a0=16.\; a^0 = 1
7.0m=07. \; 0^m = 0

Law 6 and Law 7 create a conflict when 000^0, as both give different results and both are true, so 00=\therefore 0^0 = undefined

8.a2mundefineda08. \sqrt[2m]{a} \neq undefined \to a \geq 0

Law 8 means that negative numbers cannot have even roots

9.(am)n=amn9. \; {(a^m)}^n = a^{mn}
10.ambm=(ab)m10. \; {\frac{a^m}{b^m}} = (\frac{a}{b})^m