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Chapter 1: Problem 91

Evaluate each expression without a calculator Use a calculator to check. $$[13+2(-5)]^{2}$$

Short Answer

Expert verified
9

Step by step solution

01

Simplify Inside Parentheses

Evaluate the expression inside the parentheses first. Here it is \(2(-5)\).\[2(-5) = -10\]
02

Add or Subtract Inside the Brackets

Next, add the result to 13. \[13 + (-10) = 3\]
03

Square the Result

Finally, square the result from step 2. \[3^2 = 9\]
04

Verify Using Calculator

Use a calculator to check the answer. Entering \([13 + 2(-5)]^2\) should give you 9, confirming the result.

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Key Concepts

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

Order of Operations
When evaluating algebraic expressions, it's important to follow the order of operations to get the correct answer. The order of operations can be remembered using the acronym PEMDAS, which stands for:

  • Parentheses
  • Exponents
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)
In our given exercise, you can see how PEMDAS is applied:
  • First, we evaluated inside the parentheses \(2(-5)\).
  • Next, we performed addition within the brackets \[13 + (-10)\].
  • Finally, we dealt with the exponent by squaring the result \{3^2}\.
Always follow this sequence to correctly evaluate expressions, ensuring no step is skipped or performed out of order.
Parentheses Evaluation
Evaluating expressions within parentheses is the first step in the order of operations, as it ensures that everything inside the parentheses is simplified before moving on. In our example, we started with:

  • First, evaluate \(2(-5)\). Multiplying 2 by -5 gives \{-10}\.
This step is crucial because if we do not simplify inside the parentheses first, it will lead to incorrect results. Remember, parentheses indicate that the operations enclosed should be performed first before any other calculations.
Exponentiation
Exponentiation involves raising a number to a power. In the example, the expression \[3^2\] requires us to square the number 3:
  • This means multiplying 3 by itself \{(3)(3) = 9}\.
Exponents play a significant role in determining how expressions grow, often rapidly. When dealing with exponents:

  • Make sure you complete all parentheses evaluations and other simpler operations before tackling the exponent.
  • Follow the order of operations religiously, as messing up the sequence, especially with exponents, will lead to major mistakes.
In our exercise, after simplifying inside parentheses and performing addition, we finally squared the result to get the final answer of \{9}\.

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Most popular questions from this chapter

Simplify each expression. $$ 3 k+5-2(3 k-4)-k+3 $$

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