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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