Powers of two

Given that \(9<2^n<2^k\), is the next sentence true or false?

It is possible that \(2^n\) and \(2^k\) have the same digits, just in different orders.

(For example the numbers \(1288, 8128\) have the same digits in an other order, but numbers \(1288, 1182\) don't have the same digits.)

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