Solve (2+1×2)²: Order of Operations with Square Numbers

Let's solve the expression $(2+1\times2)^2$ step-by-step, adhering to the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Firstly, handle the expression inside the parentheses $(2+1\times2)$:

• Within the parentheses, according to PEMDAS, we first perform the multiplication $1\times2$ which equals $2$.
• Now, the expression inside the parentheses becomes $(2+2)$.
• Next, perform the addition: $2+2=4$.

Now the expression simplifies to $4^2$.

Second, handle the exponent:

• Calculate the square of 4: $4^2 = 16$.

Thus, the final answer is $16$.