Problem 444 In the following exercises, simp... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 2: Problem 444

In the following exercises, simplify, using the order of operations. $$ (1+4)^{2} $$

Short Answer

Expert verified

Step by step solution

Solve the Expression Inside the Parentheses

First, handle the expression within the parentheses. Calculate yes-_+$1 + 4$.yesYes-Therefore, we have: $1 + 4 = 5$.

Apply the Exponent

Take the result from Step yes-1 and apply the exponent. In this case, we need to square 5: yes-5^2yes-Hence, $5^{2} = 25$.

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Key Concepts

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

Understanding Parentheses

Parentheses are used in mathematics to indicate that the operations enclosed within them should be performed first, before anything else outside the parentheses. This follows the order of operations rule, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

For example, in the expression $1 + 4$, we first solve what鈥檚 inside the parentheses. Ignoring this step can lead to incorrect results. Doing the enclosed operations first ensures that we respect the intended priorities. So, in $1 + 4$, we add 1 and 4 to get 5.

Working with Exponents

Exponents represent repeated multiplication of a base number by itself. The exponent is shown as a small number written above and to the right of the base number. For instance, in $5^{2}$, 5 is the base, and 2 is the exponent, meaning we multiply 5 by itself.

Here, \5^{2}\ translates to \5 \times 5\. Applying the exponent in our example, we take the 5 obtained from the parentheses and square it, which means multiplying 5 by itself to get 25.
Understanding exponents is crucial because they show up in many areas of math and science, affecting compound interest calculations, growth rates, and more.

Simplification in Math

Simplification in mathematics means reducing an expression to its simplest form. By following the order of operations, also known as PEMDAS, we systematically break down and simplify complex expressions to get a single numerical answer.

In our example, we first handled the parentheses to get 5. Then we applied the exponent to get our final simplified result, which is 25. Each step must follow the order of operations precisely, to ensure the correct answer.
Simplifying expressions helps make them more manageable and easily understandable, which benefits not just solving equations, but also in understanding more advanced mathematical concepts.

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91影视

In the following exercises, simplify, using the order of operations. $$ (1+4)^{2} $$

Short Answer

Step by step solution

Solve the Expression Inside the Parentheses

Apply the Exponent

Key Concepts

Understanding Parentheses

Working with Exponents

Simplification in Math

One App. One Place for Learning.

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