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Chapter 2: Problem 18

Simplify using the order of operations. $$-10-5^{2}$$

Short Answer

Expert verified
-35

Step by step solution

01

Identify the order of operations

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

Evaluate the exponent first

According to the order of operations, exponents should be evaluated before any other operations. Here, evaluate the exponent first: office{=-10-5^{2}}Calculating the exponent, office=settings_code{5^{2} = 25}.
03

Perform the subtraction

After evaluating the exponent, next, perform the subtraction: office{=-10-25}Lastly calculate office{-10-25 = -35}.

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Key Concepts

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

PEMDAS
PEMDAS is an acronym to help remember the order of operations in mathematics. It's crucial because it dictates the sequence in which calculations should be performed to get the correct result. The letters in PEMDAS stand for:
  • P: Parentheses - Solve expressions inside parentheses first.
  • E: Exponents - Next, calculate powers or roots.
  • M: Multiplication
  • D: Division
  • A: Addition
  • S: Subtraction


Multiplication and Division are performed from left to right. The same goes for Addition and Subtraction. In the problem -10 - 5虏, we first handle the exponent part. Once that鈥檚 done, we proceed to subtraction, as indicated by PEMDAS.
Exponents
Exponents are used to represent repeated multiplication of a number by itself. For instance, 5虏 means 5 multiplied by 5.
This simplifies to:
\[ 5^2 = 25 \]
When solving the original exercise, -10 - 5虏, we first need to evaluate the exponent 5虏. Using the exponent rule, 5虏 results in 25. This step is crucial and must be done before any other operations in the expression, as stated in PEMDAS.
Subtraction
Subtraction is one of the basic operations we perform when simplifying expressions. After handling exponents and other operations, subtraction is dealt with from left to right.

In our problem, once we calculate 5虏 which equals 25, the expression simplifies to -10 - 25. To perform the subtraction:
\[ -10 - 25 \]
Think of this as having -10 and then taking another 25 away. This results in -35.
Solving each piece step by step ensures we follow the correct order and arrive at the correct solution.

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Most popular questions from this chapter

Assume \(a>0\) (this means that \(a\) is positive) and \(b<0\) (this means that \(b\) is negative). Find the sign of each expression. $$|a|+|b|$$

Jennifer's checking account had \(\$ 320\) when she wrote two checks for \(\$ 150\), and one check for \(\$ 82 .\) What is her new balance?

Simplify. $$(-1)^{2}$$

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