The power is indicative of how many times you should multiply a number repeatedly to achieve your result. Its easy to look at it in expanded form below with the key concept being that anything ^0 is equal to 1 as 1 is the starting point of the expanded multiplication. It must be this was as if it was 0 then anything to the power of anything would become 0. The "1" represents placing "1" 4 on the multiplication train just as a 2 would place 2 4's on it.
4^0 = 1
4^1 = 1*4 =4
4^2 = 1*4*4 = 16
4^3 = 1*4*4*4 = 64
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Well, honey, any quotient equal to 4 to the negative fifth power is just 1 over 4 to the fifth power, which simplifies to 1 over 1024. So, grab your calculator and divide 1 by 1024, and you'll have your answer faster than you can say "Golden Girls marathon."
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Consider: i¹ = i i² = -1 i³ = -i i⁴ = 1 i⁵ = i ... The cycle of {i, -1, -i, 1} repeats with a period of 4 413 mod 4 = 1, so i⁴¹³ = i
A negative power can change "sides of the fraction" to become a positive power. For example: 5-2 = 1/52 = 1/25 In this case: 10-4 = 1/104 = 1/10,000 = 0.0001
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