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Math formulas: Roots formulas

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Notation:

a,ba , b : bases (a0,b0  if  n=2k) ( a \geq 0 , b \geq 0 ~~\text{if} ~~ n = 2k )

n,mn , m : powers

Formulas

(an)n=a \left( \sqrt[\scriptstyle n]{a} \right)^n = a
(an)m=amn \left( \sqrt[\scriptstyle n]{a} \right)^m = \sqrt[\scriptstyle n]{a^m}
anm=anm \sqrt[\scriptstyle m]{ \sqrt[\scriptstyle n]{a}} = \sqrt[\scriptstyle {n m}]{a}
(amn)p=anpn \left( \sqrt[\scriptstyle n]{a^m} \right)^p = \sqrt[\scriptstyle n]{a^{n p}}
amn=anpnp \sqrt[\scriptstyle n]{a^m} = \sqrt[\scriptstyle n p]{a^{n p}}
1an=an1na \frac{1}{\sqrt[\scriptstyle n]{a}} = \frac{ \sqrt[\scriptstyle n]{a^{n-1}}}{a}
abn=anbn \sqrt[\scriptstyle n]{ab} = \sqrt[\scriptstyle n]{a} \cdot \sqrt[\scriptstyle n]{b}
abn=anbn \sqrt[\scriptstyle n]{\frac{a}{b}} = \frac{\sqrt[\scriptstyle n]{a}}{\sqrt[\scriptstyle n]{b}}
anbm=ambnnm \frac{\sqrt[\scriptstyle n]{a}}{\sqrt[\scriptstyle m]{b}} = \sqrt[\scriptstyle {nm}]{\frac{a^m}{b^n}}
anbm=ambnnm \sqrt[\scriptstyle n]{a} \cdot \sqrt[\scriptstyle m]{b} = \sqrt[\scriptstyle{nm}]{a^m b^n}
a±b=a+a2b2±aa2b2 \sqrt{ a \pm \sqrt{b}} = \sqrt{ \frac{a + \sqrt{a^2 - b}}{2}} \pm \sqrt{ \frac{a - \sqrt{a^2 - b}}{2}}
1a±b=abab \frac{1}{\sqrt{a} \pm \sqrt{b}} = \frac{\sqrt{a} \mp \sqrt{b}}{a-b}

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