(3 −8 ⋅7 3 ) −2 =

Jasonbradley

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Jun 16, 2024

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Solving (3 −8 ⋅7 3 ) −2 =

This problem requires understanding the order of operations, often remembered by the acronym PEMDAS or BODMAS. Let's break down the steps:

Order of Operations

1. Parentheses/Brackets: We have a set of parentheses: (3 −8 ⋅7 3 ). We'll solve what's inside first.
2. Exponents/Orders: Inside the parentheses, we have an exponent: 7 3. This means 7 multiplied by itself three times (7 x 7 x 7).
3. Multiplication and Division: Next, we perform the multiplication: 8 ⋅7 3.
4. Addition and Subtraction: Finally, we perform the subtraction inside the parentheses.
5. Exponent: After dealing with the parentheses, we have a final exponent: the result of the parentheses raised to the power of -2.

Step-by-Step Solution

1. 7 3 = 7 x 7 x 7 = 343
2. 8 ⋅7 3 = 8 ⋅343 = 2744
3. 3 −8 ⋅7 3 = 3 −2744 = -2741
4. (-2741) -2 = 1/(-2741)2 = 1/7511681

The Answer

Therefore, (3 −8 ⋅7 3 ) −2 = 1/7511681.