Problem 53 - Algebra A Combined Function

Question

Simplify each expression. \((3-6)+4^{2}\)

Step-by-Step Solution

Answer

The simplified expression is 13.

Step 1: Solve the Parenthesis

The expression in the parenthesis is \[3-6\]Calculate this by subtracting 6 from 3, which gives you \[-3\]

Step 2: Evaluate the Exponentiation

Now look at the exponentiation in the expression, which is \[4^2\]Calculate this by multiplying 4 by itself:\[4 \times 4 = 16\]

Step 3: Combine the Results

With the evaluated results from the previous steps, combine them into the expression:\[(-3) + 16\]Perform the addition to find the result:\[-3 + 16 = 13\]

Key Concepts

Order of Operations

When simplifying expressions like \((3-6)+4^{2}\), it's essential to follow the order of operations to arrive at the correct answer. The order of operations is a set of rules that ensures calculations are carried out in the right sequence. This is often remembered using the acronym PEMDAS:

• Parentheses
• Exponents
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

First, tackle any calculations inside parentheses. Once parentheses are simplified, move on to any exponentiation involved in the expression. After that, handle multiplication and division. Lastly, perform addition and subtraction to complete the calculation.

Algebraic Expressions

Algebraic expressions consist of numbers, symbols, and operators that represent mathematical relationships. They can be simple like \(3x + 2\) or more complex like \((3-6)+4^{2}\). Each part of an algebraic expression plays a specific role:

• Numbers: Constants, which have a fixed value
• Symbols: Variables that can take different values
• Operators: Symbols such as \(+, -, \times, \div, \) and others that indicate mathematical operations

Understanding how to interpret and simplify algebraic expressions is crucial in algebra. By identifying and simplifying each component correctly, one can determine the expression's simplified form or value.

Exponentiation

Exponentiation is the mathematical operation involving two numbers, the base and the exponent. It means multiplying the base by itself as many times as indicated by the exponent. In our example, \(4^2\) means multiplying 4 by itself:

• \(4 \times 4 = 16\)

Here, 4 is the base, and 2 is the exponent. Exponentiation is a key operation in math, which not only helps in simplifying expressions but also has applications in various fields such as science, engineering, and finance. When evaluating expressions with exponents, always perform this step after simplifying any parentheses and before handling addition, subtraction, multiplication, or division.