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Chapter 1: Problem 87

\(5^{2}\)

Short Answer

Expert verified
The result of \(5^2\) is 25.

Step by step solution

01

- Understand the Problem

The exercise asks to calculate the value of the exponentiation expression: \(5^2\).
02

- Identify the Base and Exponent

In the expression \(5^2\), 5 is the base and 2 is the exponent.
03

- Apply the Exponentiation Rule

Exponentiation means multiplying the base by itself as many times as indicated by the exponent. So, \(5^2\) means 5 multiplied by itself 2 times.
04

- Perform the Multiplication

Multiply 5 by itself: \(5 \times 5\).
05

- Write the Result

The product of \(5 \times 5\) is 25.

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Key Concepts

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

base and exponent
In the context of exponentiation, understanding the base and exponent is crucial. Think of the base as the main number you are working with. In our exercise, the base is 5.
The exponent, however, tells you how many times to use the base in a multiplication. Here, the exponent is 2.
So in the expression: \(5^2\), the '5' is the base and the '2' is the exponent.
This means that you will multiply the base, 5, by itself, 2 times.
multiplication
Multiplication is one of the basic arithmetic operations. It involves combining quantities in groups.
In exponentiation, the use of multiplication is expanded. For example, in \(5^2\), you use multiplication to combine the base number, 5, with itself the number of times indicated by the exponent, 2.
In other words, you will perform the calculation 5 multiplied by 5.
This concept is essential for understanding how exponentiation works.
calculating squares
Calculating squares is a special case of exponentiation where the exponent is 2.
The term 'square' comes from the geometric idea of creating a square with equal sides.
When you square a number, you are essentially finding the area of a square with sides of that length.
For \(5^2\), you multiply 5 by itself: \(5 \times 5\), which equals 25.
So, squaring a number means multiplying it by itself to get the result. It's a handy way to deal with numbers in both arithmetic and geometry.

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