Simplify the expression 8² +9(12÷3 x 2)-7 Explain each of your steps.
8² +9(12÷3 x 2)-7
64 +9(4 x 2)-7
I think you get the picture, eh?
To simplify the expression 8² + 9(12÷3 x 2) - 7, we follow the order of operations, which is often represented by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Let's break it down step by step:
Step 1: Evaluate the exponents
The expression has one exponent, which is 8² (8 squared). To simplify this, we calculate 8² as 8 multiplied by itself: 8² = 8 x 8 = 64.
So our expression becomes: 64 + 9(12÷3 x 2) - 7.
Step 2: Evaluate the division
Next, we evaluate the division within the parentheses. 12 ÷ 3 equals 4.
The expression now becomes: 64 + 9(4 x 2) - 7.
Step 3: Evaluate the multiplication
Now we calculate the multiplication within the parentheses. 4 x 2 equals 8.
The expression simplifies to: 64 + 9(8) - 7.
Step 4: Evaluate the multiplication outside the parentheses
We can multiply 9 by 8: 9(8) = 72.
Now, the expression becomes: 64 + 72 - 7.
Step 5: Evaluate the addition and subtraction
Finally, we add and subtract the remaining terms. 64 + 72 equals 136, and subtracting 7 from 136 gives us 129.
So the simplified expression is 129.
The step-by-step breakdown helps to ensure that we apply the order of operations correctly and arrive at the correct answer of 129.