–12 ÷ 3 • (–8 + (–4)2 – 6) + 2
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–12 ÷ 3 • (–8 + (–4)2 – 6) + 2 = -9 * (-8 -8 -6) + 2 = -9 * (-22) + 2 = 198 + 2 = 200
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To solve the given expression -12 ÷ 3 • (–8 + (–4)2 – 6) + 2, we need to follow the order of operations, which is often remembered using the acronym PEMDAS. This stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
Let's break down the expression step by step:
1. Within the parentheses, we have -8 + (–4)2 – 6. First, we need to solve the exponent (-4)2, which means (-4) multiplied by itself. Applying the rule, we get 16.
2. Now we have -8 + 16 - 6. We can simplify this further by performing addition and subtraction from left to right. First, we add -8 and 16, which gives us 8.
3. Now we have 8 - 6. Subtracting 6 from 8 gives us 2.
4. The expression now becomes -12 ÷ 3 • 2 + 2. Next, we need to perform the division operation -12 ÷ 3. Dividing -12 by 3 gives us -4.
5. The expression becomes -4 • 2 + 2. Now we perform the multiplication operation -4 • 2, which gives us -8.
6. The expression finally becomes -8 + 2. Adding -8 and 2 gives us -6 as the final answer.
So, the value of the expression -12 ÷ 3 • (–8 + (–4)2 – 6) + 2 is -6.