Problem 73 - Prealgebra

Question

Simplify. $$6^{2}$$

Step-by-Step Solution

Answer

The simplified form of \(6^2\) is 36.

Step 1: Understand the Expression

The given expression is a power: \(6^2\). This means that \(6\) is being multiplied by itself.

Step 2: Perform Multiplication

Calculate \(6\) multiplied by \(6\). \(6 \times 6 = 36\).

Step 3: Write the Final Simplified Result

The expression \(6^2\) simplifies to \(36\).

Key Concepts

Understanding Powers of Numbers

Powers of numbers express repeated multiplication of a number by itself. It is composed of two main parts: the base and the exponent. In the expression \(6^2\), 6 is the base, and 2 is the exponent, which indicates that the base is used as a factor twice. This is crucial to understand because the exponent tells us how many times to multiply the base number.
The notation \(6^2\) effectively represents \(6 \times 6\). Knowing this helps us see powers as a form of shorthand for multiplication. This concept is fundamental, especially when dealing with larger exponents, as it provides a concise and efficient way to express such calculations.

Simplifying Expressions Involving Exponents

Simplifying expressions with exponents involves performing the multiplications that the exponent indicates. In this case, simplifying \(6^2\) means calculating \(6 \times 6\). The goal of simplification is to express the number in its simplest and most understandable form, which here results in 36.
When simplifying, it's essential to follow the order of operations: exponents should be resolved before performing addition, subtraction, or other operations in a broader mathematical expression. This ensures accuracy and consistency in your computations, especially in more complex expressions.

The Role of Multiplication in Powers

Multiplication is at the core of how powers work. When we talk about \(6^2\), it is simply saying 6 times 6. Understanding this highlights how multiplication builds the foundation for powers of numbers.
In more complex math problems, recognizing that an exponent represents repeated multiplication simplifies the process of computation. Consider that for \(6^3\), it would mean \(6 \times 6 \times 6\). Grasping this repetitive nature makes it easier to handle larger bases and exponents, as well as simplifying expressions with more confidence. Ultimately, seeing powers as products of repeated multiplication helps demystify what they represent.