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Chapter 2: Problem 42

Simplify using the order of operations. $$14-4^{2}+2-10$$

Short Answer

Expert verified
The simplified expression is -10.

Step by step solution

01

- Identify the Order of Operations

The order of operations can be remembered with PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
02

- Resolve Exponents

Look for any exponents in the expression. Here, resolve the exponent first: 4^2 = 16 Therefore, the expression becomes: 14 - 16 + 2 - 10
03

- Perform Addition and Subtraction from Left to Right

Now, handle addition and subtraction from left to right: 14 - 16 = -2 Then, -2 + 2 = 0 Lastly, 0 - 10 = -10

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

PEMDAS
To solve mathematical expressions correctly, we follow the order of operations. This is often remembered using the acronym PEMDAS. It stands for:
  • Parentheses
  • Exponents
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)
This order ensures that everyone gets the same result when simplifying expressions. Parentheses are handled first, which means any operations inside them are completed before anything outside. Next, we resolve exponents. After that, we handle multiplication and division, working from left to right. Finally, we perform addition and subtraction from left to right. For the given exercise, there are no parentheses, so we move on to exponents.
Simplifying Expressions
Simplifying expressions involves breaking them down step by step according to the order of operations. Let's go through the given exercise step by step.
The original expression is:
14 - 4^2 + 2 - 10
In Step 2, we handle the exponent first:
4^2 = 16
So the expression becomes: 14 - 16 + 2 - 10
Next, in Step 3, we perform addition and subtraction from left to right:
14 - 16 = -2
Then, -2 + 2 = 0
Finally, 0 - 10 = -10
Simplifying expressions can sometimes look tricky, but when you follow the order of operations, each step becomes more manageable. Remember to work left to right for multiplication and division, then for addition and subtraction.
Exponents
Exponents signify how many times a number, called the base, is multiplied by itself. In the example expression 14 - 4^2 + 2 - 10, the exponent is '2' and the base is '4'. To resolve the exponent, you calculate the base raised to the power: 4^2 means 4 multiplied by 4, which equals 16. Replacing the exponential term with 16 simplifies our expression.
So after resolving the exponent, the expression changes from: 14 - 4^2 + 2 - 10 to 14 - 16 + 2 - 10.
By simplifying exponents first, we reduce the complexity of the expression early in the process. This is aligned with the PEMDAS method and ensures accuracy in further steps.

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