Why every number to the power of 0 is equal to 1?

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I’m too dumb to get it

In: Mathematics

31 Answers

Anonymous 0 Comments

Take

4^(5) = 4*4*4*4*4

4^(4) = 4*4*4*4

4^(3) = 4*4*4

4^(2) = 4*4

4^(1) = 4

4^(0) = 1

Going up in power means you multiply

4^(4) = 4^(3) * 4

Going down in power means you divide

4^(3) = 4^(4) / 4

So you can even extend this to negative numbers

4^(0) = 1

4^(-1) = 4^(0) /4 = 1/4

4^(-2) = 4^(-1) /4 = [ 1/4 ]/4 = 1/(4*4)

4^(-3) = 4^(-2) /4 = [ 1/(4*4) ]/4 = 1/(4*4*4)

4^(-4) = 4^(-3) /4 = [ 1/(4*4*4) ]/4 = 1/(4*4*4*4)

4^(-5) = 4^(-4) /4 = [ 1/(4*4*4*4) ]/4 = 1/(4*4*4*4*4)

Keep in mind dividing a fraction:

[ 1/2 ]/2

is the same as multiplying the denominator

[ 1/2 ]/2 = 1/(2*2) = 1/4

-“A half of a half is a fourth”-

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