## Trigonometry (11th Edition) Clone

Adopting the Rule of Exponents and $i^2$ = -1 property, $i^{-42}$ works out to be $-1$.
$i^{-42}$ = $\frac{1}{i^{42}}$ (Rule of Exponents : Negative Exponent) $\frac{1}{i^{42}}$ = $\frac{1}{(i^2)^{21}}$ (Rule of Exponents : Power of a Power Rule and taking the $i^2$ = -1 property) $\frac{1}{(i^2)^{21}}$ = $\frac{1}{(-1)^{21}}$ ($i^2$ = -1) $\frac{1}{(-1)^{21}}$ = $\frac{1}{-1}$ (Odd power of -1) Therefore, $i^{-42}$ = $-1$