Surds & Indices

Laws of indices

$$a^m a^n = a^{m+n}, \quad \frac{a^m}{a^n}=a^{m-n}, \quad (a^m)^n=a^{mn}, \quad a^0=1, \quad a^{-n}=\frac{1}{a^n}, \quad a^{\frac{m}{n}}=\left(\sqrt[n]{a}\right)^m$$ So $8^{2/3}=(\sqrt[3]{8})^2=4$ and $5^{-2}=\frac{1}{25}$.