Hexadecimal to Decimal and Binary

Chaps,
I’ve been writing out the place value systems for binary, decimal and hexadecimal and have spotted a pattern that I can’t explain.

For instance…

In Binary - 2 ^ 3 = 1000
In Decimal - 10 ^ 3 = 1,000
In Hexadecimal - 16 ^ 3 = 1000

All results are 1000 even though this is expressed in the three different number systems so are different values.

The pattern repeats no matter what the next power of is:

In Binary - 2 ^ 7 = 10000000
In Decimal - 10 ^ 7 = 10,000,000
In Hexadecimal - 16 ^ 7 = 10000000

This is more of an observation that a question I suppose but if anyone can offer an explanation as to why this occurs then I’d appreciate it!

Cheers,

Gareth.