## Intermediate Algebra for College Students (7th Edition)

Published by Pearson

# Chapter 7 - Section 7.7 - Complex Numbers - Exercise Set - Page 570: 96

#### Answer

$-1$

#### Work Step by Step

Note that $(-i) = -1(i)$ Thus, the given expression is equivalent to: $=[-1(i)]^6$ Use the rule $(ab)^m = a^mb^m$ to obtain: $=(-1)^6(i)^6 \\=1(i^6) \\=i^6$ RECALL: (1) $a^{mn} = (a^m)^n$ (2) $i^2=-1$ (3) $a^{m+n} = a^m \cdot a^n$ Use rule (1) above to obtain: $i^{6}=(i^2)^{3}$ Use rule (2) above to obtain: $=(-1)^{3} \\=(-1)(-1)(-1) \\=-1$

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