The value of (4²)²$+4\times 4÷4-4$ is:

To find the value of the given expression, let us write it down clearly:
${\left(4^2\right)}^2+4\times 4÷4-4$

We can solve this expression step-by-step by following the order of operations (PEMDAS/BODMAS):

Step 1: Simplify the exponent term
Using the power of a power rule, ${\left(a^m\right)}^n=a^{m\times n}$, we simplify the first term:
${\left(4^2\right)}^2=4^{2\times 2}=4^4=256$

Now, substitute this back into the expression:
$256+4\times 4÷4-4$

Step 2: Perform the division
Next, we perform the division operation ($4÷4$):
$4÷4=1$

Substituting this result, our expression becomes:
$256+4\times 1-4$

Step 3: Perform the multiplication
Now, perform the multiplication ($4\times 1$):
$4\times 1=4$

Substituting this back, we get:
$256+4-4$

Step 4: Perform the addition and subtraction
Finally, perform the addition and subtraction from left to right:
$256+4=260$
$260-4=256$

Step 5: Match the final value with the options
The calculated value is $256$.
Expressing $256$ as a power of 4:
$256=4^4$

Therefore, the correct option is 4⁴.