Problem 48 - Algebra 1

Question

Evaluate the expression. \(\left(3^{3}-20\right)^{2}\)

Step-by-Step Solution

Answer

The value of the expression \(\left(3^{3}-20\right)^{2}\) is 49.

Step 1: Calculate the Exponent

First, calculate \(3^{3}\), which equals to 27.

Step 2: Subtract 20

Next, subtract 20 from 27. The result is 7.

Step 3: Square the Result

Finally, square the result. That is, find the product of 7 and 7. The result is 49.

Key Concepts

Evaluating Expressions

Evaluating expressions is like solving a puzzle. It means finding the value of an expression by performing mathematical operations. Expressions can include numbers, variables, and operators like addition, subtraction, multiplication, and division.
In our example, o the expression o o o . , looks complex, but it just needs some orderly steps to solve it. By breaking it down:

• Power: The exponent
• Subtraction: After finding the power value, subtracting the next number simplifies the expression.
• Exponents: Finally, applying an exponent again completes the evaluation.

Following these steps allows us to successfully evaluate the expression, giving simplicity to what might initially look difficult.

Order of Operations

The order of operations is a rule that tells you the sequence in which to solve different parts of a math problem. Math often requires us to follow a specific order so that everyone solves a problem the same way. This prevents confusion over which operations to do first. The most common acronym used is PEMDAS, standing for:

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

For the expression , we apply the rules:
1. inside parentheses is addressed first, starting with its exponent.
2. Subtraction follows the solution of exponents within parentheses.
3. Another exponent is applied outside the parentheses, completing the operation.
This framework ensures the expression is solved in an orderly manner without error.

Algebraic Concepts

Algebraic concepts involve using symbols and letters to represent numbers and quantities in equations and expressions. It's like a universal language in math that helps in generalizing arithmetic operations. Here we focused on numbers, but variables work the same way in expressions.
An expression like gives you a set of steps to find the final value. By using algebraic principles and applying them to different operations:

• Exponents in
• Arithmetic operations, like subtracting and squaring the result.

These steps show fundamental algebraic processes. Understanding these concepts helps students to analyze, simplify, and ultimately solve expressions and equations efficiently. By mastering these, tackling even more complex algebraic problems becomes manageable.