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Chapter 1: Problem 74

Evaluate:\(3+4^{2}\)

Short Answer

Expert verified
19

Step by step solution

01

Express the Problem

We start with the problem expression: \(3 + 4^2\). Our goal is to find the numerical value of this expression.
02

Calculate the Exponentiation

Evaluate \(4^2\), which means 4 raised to the power of 2. Thus, \(4^2 = 4 \times 4 = 16\).
03

Perform the Addition

Now, substitute the result from the power calculation back into the original expression. So, we have \(3 + 16\). Add these two numbers to get the final result: \(3 + 16 = 19\).

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Key Concepts

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

Exponentiation
Exponentiation is a mathematical operation that involves raising a number, known as the base, to a power, which is an exponent. In simple terms, exponentiation tells you how many times a number is multiplied by itself. For example, in the expression \(4^2\), the base is 4, and the exponent is 2. This means you multiply 4 by itself once:
  • \(4^2 = 4 \times 4\)
  • Resulting in \(16\)
Understanding exponentiation is crucial as it is often used in various mathematical and real-world applications, such as geometry and science.
Addition
Addition is one of the most fundamental arithmetic operations. It is the process of finding the total or sum by combining two or more numbers.
  • For instance, in the given problem, after calculating \(4^2\), we obtained 16.
  • We then added this result to 3, as shown: \(3 + 16\).
  • The sum of these numbers is 19.
Addition is essential because it forms the basis for other mathematical concepts and operations, making it a key skill to practice and master.
Problem-solving in Mathematics
Problem-solving in mathematics involves understanding and dissecting a problem to find a solution. Here鈥檚 how you can tackle problems like the exercise given:
  • **Identify:** Determine what the problem is asking. In this case, evaluate \(3 + 4^2\).
  • **Plan:** Figure out which operations are needed鈥攊n this problem, exponentiation and addition.
  • **Execute:** Perform the calculations. First, solve \(4^2 = 16\). Then, add 3 to 16.
  • **Review:** Check your work to ensure accuracy鈥攐ur final answer is 19.
Strong problem-solving skills allow you to tackle complex problems efficiently and effectively.
Numerical Expressions
A numerical expression is a mathematical phrase that consists of numbers and operations, such as addition or exponentiation. In the exercise \(3 + 4^2\), the expression involves:
  • A constant number (3)
  • An exponentiation (\(4^2\))
  • An addition operation between the two
Evaluating numerical expressions requires understanding the sequence of operations. It鈥檚 important to respect the order of operations, commonly remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). By following the correct order, you ensure that the expression is simplified accurately.

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Most popular questions from this chapter

Calculate and express each result in its simplest form:\(3+(-4)\)

Calculate and express each result in its simplest form:\(3-(-4)\)

Express as decimal fractions:\(\frac{5}{32}\)

Factorize in prime numbers:80

Calculate and express each result in its simplest form:\(8 \div(-4)\)
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