#powers of 5

[er-cryptid]

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This is a thing I've noticed:

2^(-1) = .5; 5^(1) = 5 2^(-2) = .25; 5^(2) = 25 2^(-3) = .125; 5^(3) = 125 2^(-4) = .0625; 5^(4) = 625 etc.

And you know what else?

5^(-1) = .2; 2^(1) = 2 5^(-2) = .04; 2^(2) = 4 5^(-3) = .008; 2^(3) = 8 4^(-4) = .0016; 2^(4) = 16 etc.

Does anybody know if there's a name for this?  I think that the most appropriate expression of this apparent rule (assuming it applies for another pair of numbers)

a^(-n) = b^(n)*10^(-n)

or more in an actual rule sort of way (at least as it appears)

if a^(-n) = b^(n)*10^(-n), then b^(-n) = a^(n)*10^(-n)

though depending on one's point of view I believe it would also work as

if a^(n) = b^(-n)*10^(n), then b^(n) = a^(-n)*10^(n)

But that's not the point. Does this have a name?