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Chapter 1: Problem 121

In the following exercises, simplify using the order of operations. $$ 3^{2}+7^{2} $$

Short Answer

Expert verified
58

Step by step solution

01

- Evaluate Exponents

Start by evaluating the exponents in the expression. Calculate each term separately. For the expression: 3^{2} = 9 7^{2} = 49
02

- Perform Addition

Next, add the results of the evaluated exponents together. 9 + 49 = 58

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Key Concepts

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

Exponents
Exponents are a way to express repeated multiplication of a number by itself. For instance, 3^{2} means you multiply 3 by itself: 3 * 3. This equals 9. Similarly, 7^{2} means you multiply 7 by itself: 7 * 7, which equals 49.

To properly simplify an expression involving exponents, always start by calculating the exponents first. This process is part of the order of operations in mathematics.
Addition
Addition is a fundamental arithmetic operation used to combine values. After evaluating any exponents in an expression, the next step is to add the results.

In our example, after computing 3^{2} and 7^{2}, we obtained 9 and 49 respectively. To finalize the expression, we add these values:
  - 9 + 49 = 58

Addition helps to combine individual calculated components into a final value, simplifying the expression fully.
Simplification
Simplification involves reducing an expression to its simplest form. The process follows the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

In our example:
  • First, we calculate the exponents: 3^{2} = 9 and 7^{2} = 49.
  • Second, we perform the addition: 9 + 49 = 58.
Breaking down each part of the expression and computing step-by-step ensures accuracy. Following these rules ensures any mathematical expression is simplified correctly.

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