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Simplify the following expression:

(2^999 x 3^1000)÷{[(2^50)^20]x[(3^333)^3]}

Showing this, (2^999 x 3^1000)÷{[(2^50)^20]x[(3^333)^3]},

the 1st thing to do is simplify the denominator.

It is known that (2^50)^20 is the same as 2^(50*20) = 2^1000.

It is known the (3^333)^3 = 3^(333*3) = 3^999.

Our original problem is then (2^999 x 3^1000)÷(2^1000 x 3^999).

This can be rewritten as (2^999/2^1000)*(3^1000/3^999).

That can then be rewritten as [2^(999-1000)]*[3^(1000-999)].

Again we can rewrite it as [2^-1][3^1)].

My final answer is then (1/2)3 = 3/2.

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