# How do you simplify i^6?

We know that ${i}^{2} = - 1$ hence
${i}^{6} = {\left({i}^{2}\right)}^{3} = {i}^{2} \cdot {i}^{2} \cdot {i}^{2} = \left(- 1\right) \cdot \left(- 1\right) \cdot \left(- 1\right) = - 1$