The given expression is:

$[(-2)^4]^3$

Step 1: Apply the Power of a Power Property

The power of a power property states:

$(a^m)^n = a^{m \cdot n}$

Applying this property:

$[(-2)^4]^3 = (-2)^{4 \times 3} = (-2)^{12}$

Step 2: Simplify the Exponentiation

Since the exponent is even, we know:

$(-2)^{12} = 2^{12}$

since raising a negative base to an even power results in a positive value.

Thus, the equivalent expression is:

$2^{12}$

Let me know if you need further explanation!

Related Questions:

1. What is the numerical value of $2^{12}$?
2. How does the power of a power property work with negative bases?
3. What happens when an odd exponent is applied to a negative base?
4. Can the expression $[(-3)^5]^2$ be simplified similarly?
5. How would the result change if the base were positive instead?

Tip: Always check whether an exponent is even or odd when dealing with negative bases!