Problem 80 - Prealgebra

Question

Perform the indicated operations. $$6^{2}$$

Step-by-Step Solution

Answer

The result of \(6^2\) is 36.

Step 1: Understand Exponent Notation

The expression provided is \(6^2\), which means that "6" is the base and "2" is the exponent. The exponent tells us how many times to multiply the base by itself.

Step 2: Apply Exponentiation

To solve \(6^2\), multiply the base by itself the number of times indicated by the exponent. In this case, multiply 6 by itself once: \(6 \times 6\).

Step 3: Calculate the Product

Now, perform the multiplication: \(6 \times 6 = 36\). This gives us the result of \(6^2\).

Key Concepts

Base and Exponent

Understanding the concepts of base and exponent is essential when dealing with exponentiation. In mathematical expressions like \(6^2\), the number 6 is called the **base**. The base is the number that will be multiplied.The number 2, positioned as a small numeral to the top right of the base, is the **exponent**. The exponent tells us how many times the base is multiplied by itself. For example, in this case:

• Base = 6
• Exponent = 2

By clearly understanding base and exponent, you will find most exponentiation problems easy to solve.

Multiplication

To solve exponentiation problems like \(6^2\), you need to understand multiplication. The process of exponentiation is essentially repeated multiplication of the base.In our example, \(6^2\) signifies multiplying the base by itself according to the number of times specified by the exponent. Here, perform the operation:

• Step 1: Identify the base (6)
• Step 2: Multiply 6 by itself, since the exponent is 2: \(6 \times 6\)

Once you've completed this multiplication step, you get the result quicker, making more complex calculations manageable.

Power of a Number

The term "power of a number" refers to the result obtained when a number (the base) is raised to the power of an exponent. For \(6^2\), you find the power by multiplying as per the guidelines of exponentiation. The expression \(6^2\) becomes the power of 6 owing to the exponent 2. This is understood as the product of 6 multiplied two times:

• First multiplication: \(6 \times 6 = 36\)

Hence, \(6^2 = 36\), which is the power of the number 6 when squared.Recognizing a power as the output of multiplying the base according to its exponent helps reinforce your grasp on foundational math skills. This comprehension simplifies handling powers of numbers in various mathematical scenarios.