Answer: [tex]-i[/tex]Step-by-step explanation: You need to remember: 1. The Product of powers property: [tex](a^m)(a^n)=a^{(m+n)}[/tex] 2. The Power of a power property: [tex](a^m)^n=a^{mn}[/tex] In this case, given: [tex]i^{15}[/tex] You need to follow these steps in order to simplify it: 1. Apply the Product of powers property: [tex]i^{15}=i^{12}i^2i[/tex] 2. Apply the Power of a power property: [tex](i^{4})^3i^2i[/tex] 3. Finally, since [tex]i^4=1[/tex] and [tex]i^2=-1[/tex], you get: [tex]=(1)(-1)(i)=-i[/tex]