Simplify each power of i. 1/i^-12

Question

Accepted Answer

Hello everyone in this video we're going to be looking at this practice problem where we want to simplify one divided by eye to the -152 power. So in this case you can see that we have a negative exponent in the denominator of a fraction. So in order to make it positive we can bring it back up to the numerator. So one Divided by eye to the -152 can be written as I To the positive 152. So now that I brought it back up we want to think about what I represents. So recall that I is the imaginary number, the square root of negative one. So that means that when I have I squared I have the square root of negative one times the square root of negative one which simplifies To just -1. So in order to simplify, I took the 152. I want to try to pull out as many I squared I to the second power as I can because I know that I to the second power is a real number of negative one. So if I want to pull out as many I squared as I can, I'll write I to the second power And Because I need to multiply by this number, I need two times X. To equal my original power which is 152. So if I solve for X and see that I get 76. So this becomes I to the second power To the 70 76th power. But if I replace I squared with negative one, this becomes negative one to the power of 76. And because I'm raising a negative number to an even power, I end up getting back a positive number of one. Because I have negative one times negative one is equal to positive one. So I end up getting just one, which means that one divided by I to the -152 power is actually equal to just one. So this becomes my final answer and you can see that if we look at the answer choices, this aligns with answer choice C. So hopefully this video helped and see you next time.

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Simplify each power of i. 1/i^-12

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