Problem 87
Question
\(5^{2}\)
Step-by-Step Solution
Verified Answer
The result of \(5^2\) is 25.
1Step 1 - Understand the Problem
The exercise asks to calculate the value of the exponentiation expression: \(5^2\).
2Step 2 - Identify the Base and Exponent
In the expression \(5^2\), 5 is the base and 2 is the exponent.
3Step 3 - 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.
4Step 4 - Perform the Multiplication
Multiply 5 by itself: \(5 \times 5\).
5Step 5 - Write the Result
The product of \(5 \times 5\) is 25.
Key Concepts
base and exponentmultiplicationcalculating squares
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.
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.
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.
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.
Other exercises in this chapter
Problem 86
Explain why \(7 a^{2} b\) and \(5 a b^{2}\) are not like terms.
View solution Problem 86
\(\frac{15-3}{2+4}\)
View solution Problem 87
A student said that the expression \((5 x)(3 y)\) cannot be simplified because \(5 x\) and \(3 y\) are not like terms. Explain why the student is wrong.
View solution Problem 87
\(\frac{14-2^{2}}{6+4}\)
View solution