When the expression $(2^1)(2^2)(2^3)\cdots (2^{99})(2^{100})$ is written as an integer, what is the product of the tens digit and the ones digit?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
When the expression $(2^1)(2^2)(2^3)\cdots (2^{99})(2^{100})$ is written as an integer, what is the product of the tens digit and the ones digit?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
8
When the expression $(2^1)(2^2)(2^3)\cdots (2^{99})(2^{100})$ is written as an integer, what is the product of the tens digit and the ones digit?
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