Problem 32 Simplify using the order of oper... [FREE SOLUTION]

91影视

Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

1 Edition

Chapter 2: Problem 32

Simplify using the order of operations. $$-5+(3-10)^{2}$$

Short Answer

Expert verified

The simplified result is 44.

Step by step solution

Evaluate the expression inside the parentheses

First, solve the expression inside the parentheses: $3 - 10 = -7$

Apply the exponentiation

Next, apply the exponentiation to the result from Step 1: $(-7)^{2} = (-7) \cdot (-7) = 49$

Perform the remaining addition

Finally, combine the result from Step 2 with the number outside the parentheses: $-5 + 49 = 44$

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Key Concepts

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

simplifying expressions

Simplifying expressions involves breaking down a complex formula into simpler parts. This often includes applying various mathematical operations like addition, subtraction, exponentiation, and more. The goal is to make the expression easier to work with and understand. In our exercise, simplicity is achieved by carefully following the order of operations. Each step reduces complexity until we reach the final, simplified result. Always start simplifying from the innermost part of the expression and move outward. For example, handle parentheses before you address addition or multiplication.

parentheses

Parentheses are crucial in guiding the order of operations. They tell you which part of an expression to solve first. Whenever you see parentheses, handle the calculations inside them before moving on to other operations. In our example, the expression inside the parentheses is (3 - 10). Solving what's inside the parentheses first, we get -7. Treat parentheses like signposts; they help prioritize what to solve first to avoid mistakes in more complex expressions.

exponentiation

Exponentiation refers to raising a number to the power of another number. In simpler terms, this means multiplying the number by itself a certain number of times. In our exercise, after solving the parentheses, we had (-7). Next, we squared (-7), which means multiplying (-7) by itself. So, (-7)^2 = (-7) * (-7) = 49. Exponentiation is a powerful tool and must be handled right after dealing with any parentheses but before performing addition or subtraction.

addition

Addition is often the final step when simplifying expressions containing multiple operations. Once you have solved any parentheses and applied exponentiation, you then combine the remaining values. In our example, after solving the parentheses and exponentiation, we ended up with -5 + 49. Adding these together, the final result is 44. Although addition seems straightforward, it's essential to follow the appropriate order of operations to ensure accuracy.

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91影视

Simplify using the order of operations. $$-5+(3-10)^{2}$$

Short Answer

Step by step solution

Evaluate the expression inside the parentheses

Apply the exponentiation

Perform the remaining addition

Key Concepts

simplifying expressions

parentheses

exponentiation

addition

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