Solve [(4-2)²]³: A Triple Exponent Challenge

To solve the expression $[(4-2)^2]^3$, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

Step 1: Solve the innermost parentheses:

The expression inside the innermost parentheses is $4-2$. We perform the subtraction:

$4-2 = 2$

Step 2: Apply the exponentiation:

Next, we take the result of the subtraction and apply the squaring operation $((2)^2)$:

$2^2 = 4$

Step 3: Apply the outer exponentiation:

Finally, we take the result of the previous step and raise it to the power of 3:

$4^3 = 64$

Therefore, the value of the expression $[(4-2)^2]^3$ is $64$.