Why is it that e.g. 4ˆ-s = 1/4 s?

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Hi! I hope my question is understandable. This is something I never quite understood.

Why is it that when you put the negative unit in the exponent that it can be translated into a fraction?

(I hope this makes sense! English is not my first language!)

Thanks in advance for the answers!

In: Mathematics

3 Answers

Anonymous 0 Comments

You keep dividing by that number and it eventually goes into fractions. A quick way to think about it is this :

4^4 = 4 x 4 x 4 x 4 = 256

4^3 = 4 x 4 x 4 = 64 and also = 256 ÷ 4

4^2 = 4 x 4 = 16 and also = 64 ÷ 4

4^1 = 4 = 4 and also = 16 ÷ 4

4^0 = 1 and also = 4 ÷ 4

4^(-1) = 1/4^1 = 1/4 and also = 1 ÷ 4

4^(-2) = 1/4^2 = 1/16 and also = (1/4) ÷ 4

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