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Chapter 1: Problem 87

Evaluate each expression without a calculator Use a calculator to check. $$(-2+5) 3^{2}$$

Short Answer

Expert verified
The value of the expression is 27.

Step by step solution

01

- Simplify the Expression Inside the Parentheses

First, simplify the expression inside the parentheses: $$-2 + 5 = 3$$.
02

- Evaluate the Exponent

Next, evaluate the exponent: $$(3^2 = 3 \times 3 = 9)$$.
03

- Multiply the Results

Multiply the simplified result of the parentheses by the result of the exponentiation: $$(3 \times 9 = 27)$$.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Simplify Expressions
Before solving algebraic expressions, it's important to simplify them step-by-step. This process involves breaking down complex expressions into simpler parts.

Start by looking for elements inside parentheses, as they take precedence.
In our example, the expression inside the parentheses is \(-2 + 5\). Simplify it by performing the operation: \(-2 + 5 = 3\).

Once this is done, the expression becomes simpler and more manageable, making further calculations easier. Remember, simplification often makes it clear what steps to follow next.
Exponentiation
Exponentiation refers to the process of raising a number to a power. In mathematical terms, if you have \(a^b\), \(a\) is the base and \(b\) is the exponent.

In our problem, we have \(3^2\). This means that 3 (the base) is multiplied by itself 2 (the exponent) times: \(3 \times 3 = 9\).

Understanding exponentiation is crucial for solving algebraic expressions, especially when they include multiple operations. Accurately calculating the exponent helps in achieving the correct final result.
Order of Operations
The order of operations is a set of rules that dictate the sequence in which calculations should be performed to achieve the correct result.

This concept is often remembered by the acronym PEMDAS:

  • P: Parentheses
  • E: Exponents
  • M/D: Multiplication and Division (from left to right)
  • A/S: Addition and Subtraction (from left to right)


In our example, we followed this order:
1. Simplify the expression inside the parentheses: \(-2 + 5 = 3\).
2. Evaluate the exponent: \(3^2 = 9\).
3. Perform the multiplication: \(3 \times 9 = 27\).

By applying the order of operations correctly, we can confidently solve any algebraic expression accurately and efficiently.

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Most popular questions from this chapter

Simplify. $$ 3 a^{2} w^{2}-5 w^{2} \cdot a^{2}-2 a w \cdot 2 a w $$

Find each product or quotient. $$ \frac{6 x^{3}}{2} $$

Combine like terms. $$ -5 x-(-2 x) $$

Write an algebraic expression for each problem. Parallelogram. The lengths of the sides of a lot in the shape of a parallelogram are \(w\) feet and \(w+50\) feet. What is its perimeter? Is it possible to find the area from this information?

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