How do you simplify $7i^40 - 9i^100$ ?

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Answer 1 · 2015-11-10T11:22:23

$7i^40 - 9i^100 = -2$

We will use two facts.

1) $x^(ab) = (x^a)^b$

2) $i^2 = -1 => i^4 = (i^2)^2 = 1$

Applying (1), we get

$7i^40 - 9i^100 = 7i^(4*10) - 9i^(4*25) = 7(i^4)^10 - 9(i^4)^25$

Then, by (2),

$7(i^4)^10 - 9(i^4)^25 = 7*1^10 - 9*1^25 = 7 - 9 =-2$

So our final result is

$7i^40 - 9i^100 = -2$

How do you simplify 7i^40 - 9i^1007i^40 - 9i^100?