Problem 1 - Elementary Algebra

Question

For exercises 1-80, evaluate. $$ 6^{2} $$

Step-by-Step Solution

Answer

36

Step 1 - Understand the Problem

The problem requires the evaluation of the exponential expression given as \(6^{2}\). This involves calculating the value when 6 is raised to the power of 2.

Step 2 - Recall the Definition

Recall that \(a^{b}\) means multiplying the base \(a\) by itself \(b\) times. In this case, \(6^{2}\) means multiplying 6 by itself 2 times.

Step 3 - Perform the Multiplication

Calculate the product of 6 multiplied by itself: \(6 \times 6 = 36\).

Key Concepts

Exponents

An exponent tells you how many times to multiply a number by itself. For example, in the expression \(6^2\), the number 6 is the base, and 2 is the exponent. The exponent 2 means we multiply 6 by itself two times. This is often referred to as 'raising 6 to the power of 2'. Exponents are a crucial part of mathematics because they allow us to write repeated multiplication compactly and understandably. Remember that the order of operations (PEMDAS/BODMAS) dictates that you perform exponentiation before multiplication, division, addition, or subtraction.

Multiplication

Multiplication is one of the basic arithmetic operations. It involves adding a number to itself a certain number of times. For example, \(6 \times 6 = 36\) means you add 6 to itself 6 times:
6 + 6 + 6 + 6 + 6 + 6 = 36. In the context of exponents, the multiplication process can be seen as a repeated addition of the base number. When you see \(6^2\), you need to multiply 6 by itself, which means:
\[6 \times 6 = 36\].
Practicing multiplication helps in understanding larger exponents and other mathematical operations.

Step-by-Step Solution

To evaluate an expression such as \(6^2\), it's helpful to follow a step-by-step solution:
Step 1: Understand the Problem - Here, you need to determine what is being asked. Knowing \(6^2\) involves calculating 6 raised to the power of 2.
Step 2: Recall the Definition - Remember that \(a^b\) means multiplying the base \(a\) by itself \(b\) times. So, \(6^2\) means \(6 \times 6\).
Step 3: Perform the Multiplication - Calculate the product by performing the repeated multiplication: \(6 \times 6\) which equals 36.
By breaking down the problem into smaller parts, it becomes easier to understand and solve. This technique can be applied to more complex expressions as well.