Problem 20 - Algebra 1: Concepts and Skills

Question

Evaluate the expression. $$ 6^{2}+4 $$

Step-by-Step Solution

Answer

The evaluation of the expression \(6^{2}+4\) is 40.

Step 1: Exponentiation

The first step is to compute the exponentiation operation. In our case, 6 to the power of 2. This is done by multiplying 6 by itself. So, \(6^{2}\) is equal to 36

Step 2: Addition

The second step is to add 4 to the result from the exponentiation operation. The addition operation is performed as 36 (result from previous operation) + 4, which equal 40.

Key Concepts

Exponentiation

When dealing with exponentiation, it refers to the mathematical operation where a number, known as the base, is multiplied by itself a specific number of times, which is called the exponent. In the expression given, 6 is the base and 2 is the exponent, written as \( 6^2 \). This means you multiply 6 by itself.To break it down:

• Base (6): The number being multiplied.
• Exponent (2): The number of times the base is used as a factor.

So, \( 6^2 = 6 \times 6 = 36 \). This step is crucial because, according to the order of operations, exponentiation is performed before addition or subtraction.

Addition

Addition is one of the most basic arithmetic operations. It involves combining two or more numbers to get a total sum or amount. In the exercise, after computing the exponentiation of 6, which is 36, we add 4 to it. This looks like:

• Expression: 36 + 4
• Result: 40

The order of operations dictates that, after resolving exponentiation, any additions should be performed next. Therefore, adding 4 gives us the final answer of 40.

Arithmetic Operations

Arithmetic operations are the basic operations that include addition, subtraction, multiplication, and division. These operations are governed by an order, commonly known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).Breaking down the operations:

• Parentheses: First solve expressions inside parentheses.
• Exponentiation: Next handle exponents, as we did with \( 6^2 \).
• Multiplication and Division: Then execute these operations from left to right.
• Addition and Subtraction: Lastly, these are performed from left to right.

Understanding this order is crucial for correctly evaluating mathematical expressions. It ensures that each step is handled in a logical manner, leading to the correct result.