Evaluate the algebraic expression 2 + 8(x - 2)^3 for x = 6.

Step-by-step solution

1. 1

   Substitute, keeping the brackets exactly as written.

   $2+8(6-2)^{3}.$

   Writing $8\cdot 6-2$ or dropping the parentheses at this point is the most common way to lose the question.

2. 2

   Simplify inside the bracket first. Grouping symbols outrank everything else:

   $6-2=4\ \Longrightarrow\ 2+8(4)^{3}.$

3. 3

   Apply the exponent before the multiplication. The cube belongs to the bracket only, not to $8\cdot 4$:

   $4^{3}=64\ \Longrightarrow\ 2+8(64).$

   Cubing $8\cdot 4=32$ instead would give $32768$ — a very different answer.

4. 4

   Multiply.

   $8\cdot 64=512\ \Longrightarrow\ 2+512.$

5. 5

   Add last.

   $2+512=514.$

   The order used — bracket, exponent, multiplication, addition — is exactly the standard hierarchy read left to right through the expression.