Chapter 10 - Exponents and Radicals - 10.8 The Complex Numbers - 10.8 Exercise Set - Page 687: 94

$-243i$

Using $i^2=-1$ and the laws of exponents, the given expression, $ (-3i)^{5} ,$ is equivalent to \begin{array}{l}\require{cancel} (-3)^5i^5 \\\\= -243i^5 \\\\= -243i^4\cdot i \\\\= -243(i^2)^2\cdot i \\\\= -243(-1)^2\cdot i \\\\= -243(1)\cdot i \\\\= -243i \end{array}