Laws of Indices

Indices:

\(\begin{aligned} &\bullet \quad a^0=1\\\\ &\bullet \quad a^{-m}=\dfrac{1}{a^m},\,a \ne 0\\\\ &\bullet \quad a^{\frac{1}{n}}=\sqrt[n]{a}\\\\ &\bullet \quad a^{\frac{m}{n}}=(\sqrt[n]{a})^m \end{aligned}\)

Law of indices:

\(\begin{aligned} &\bullet \quad (a^m)^n=a^{mn}\\\\ &\bullet \quad a^{m}\times a^n=a^{m+n}\\\\ &\bullet \quad a^{m}\div a^n=a^{m-n}\\\\ &\bullet \quad (ab)^n=a^n\times b^n\\\\ &\bullet \quad \left(\dfrac{a}{b} \right)^n=\dfrac{a^n}{b^n}, \,b\neq 0 \end{aligned}\)