Problem 76 - Prealgebra

Question

Simplify. $$5^{2}$$

Step-by-Step Solution

Answer

The simplified value of \(5^2\) is 25.

Step 1: Understanding Exponents

The term \(5^2\) in the expression is an exponent. It means 5 is multiplied by itself a certain number of times. The base here is 5 and the exponent is 2.

Step 2: Evaluate the Exponent

To evaluate \(5^2\), we multiply the base 5 by itself, i.e., \(5 \times 5\).

Step 3: Perform Multiplication

Now, compute the multiplication: \(5 \times 5 = 25\).

Step 4: Conclusion

Therefore, the simplified value of \(5^2\) is 25.

Key Concepts

Understanding Exponents

Exponents are a fundamental concept in mathematics, especially when it comes to algebra. They tell us how many times to multiply a number, which we refer to as the base, by itself.
For the expression \(5^2\), the number 5 is called the base, and 2 is the exponent. This particular exponent, often read as "five squared," instructs us to multiply the base, 5, by itself. Understanding this step lays the groundwork for simplifying expressions with exponents.

Recognizing this pattern helps with larger calculations and prepares you for more advanced mathematics topics.

The Role of Multiplication in Exponents

Multiplication plays a crucial role in working with exponents. In our example \(5^2\), the exponent tells us to perform a simple multiplication:

• Take the base (5) and multiply it by itself.
• Perform the multiplication: \(5 \times 5\).
• Calculate the result: the answer is 25.

These steps show how multiplication underpins the concept of exponents and gives us a simplified expression.

Practicing this concept with different bases and exponents will enhance your arithmetic skills and build a foundation for algebraic equations.

Basic Algebra Concepts Involving Exponents

Algebra involves using symbols and numbers to express mathematical relationships and to solve equations. Exponents are a part of this, simplifying expressions and making them more manageable.
To effectively use exponents in algebra, remember the following:

• Identify the base and the exponent in an expression.
• Perform the multiplication as the exponent indicates.
• Combine understanding of number operations to solve more complex problems.

Reinforcing these algebra basics helps you transition into more complex areas like polynomials and functions, ensuring you are well-prepared for advanced mathematical studies.