Final answer:
In Mathematics, 4⁽⁴⁾ in expanded form is 4^(4^(4^4)), which simplifies to 4^(4^256). Note the expression 4⁽⁴⁾ represents repeated exponentiation, called tetration.
Step-by-step explanation:
The question asks us to write 4⁽⁴⁾ in expanded form and then simplify. First, let's understand what this means. The notation ⁽⁴⁾ is called 'tetration', which is a hyperoperation that is essentially repeated exponentiation. So, 4⁽⁴⁾ means '4 raised to the power of 4 raised to the power of 4 raised to the power of 4'. In expanded form, it becomes: 4^(4^(4^4)).
Before simplification, we solve from top to bottom: 4^4 = 256. So, the expression simplifies to: 4^(4^256). But the further computation of this expression is not feasible because 4^256 results in an astronomically large number. So, 4^(4^256) can be considered as the simplified form of the original expression.
Learn more about Tetration