Problem 122 In the following exercises, simp... [FREE SOLUTION]

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Chapter 1: Problem 122

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

Short Answer

Expert verified

100

Step by step solution

Identify the Expression

The given expression is $ (3 + 7)^2 $.

Simplify Inside the Parentheses

First, perform the addition inside the parentheses. Compute $ 3 + 7 $. This gives $ 10 $.

Apply the Exponent

Next, apply the exponent to the result. Compute $ 10^2 $, which means $ 10 \times 10 $. This gives $ 100 $.

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Key Concepts

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

Simplifying Expressions

Simplifying an expression means to make it as basic as possible. You combine like terms and perform operations step by step. For example, in the expression $ (3 + 7)^2 $, simplifying means breaking down each part of the equation until you get a single number.
The first thing to do is often to combine any like terms. Like terms are numbers or variables with the same exponent. Simplifying ensures your expression is the simplest and most understandable form. Let's break down the specific steps more:

Parentheses

Parentheses are used to group parts of an expression that should be calculated first. In the expression $ (3 + 7)^2 $, the parentheses tell us to add 3 and 7 before doing anything else.

Always start simplifying expressions by first resolving anything within parentheses. Ignoring parentheses can lead to incorrect answers because the order of operations might be mixed:

Step 1: Simplify the part inside the parentheses, so $ 3 + 7 = 10 $.

Just remember, parentheses are your guideposts. They tell you what to wrap up first before moving on to other parts of the expression.

Exponents

Exponents indicate how many times to multiply the base number by itself. In the expression $ (10)^2 $, the exponent is 2, and the base number is 10.

Here is how exponents work (remember our parentheses example of $ (3 + 7) $):

You first solve inside the parentheses and get $ 10 $.
Then, apply the exponent: $ 10^2 = 10 \times 10 = 100 $.

Exponents can be tricky but remember the key is repetition:

For example, $ 2^3 = 2 \times 2 \times 2 = 8 $.

With exponent skills, you can simplify expressions even more efficiently and accurately.

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91影视

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

Short Answer

Step by step solution

Identify the Expression

Simplify Inside the Parentheses

Apply the Exponent

Key Concepts

Simplifying Expressions

Parentheses

Exponents

One App. One Place for Learning.

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