/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 64 Simplify the given expression. ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 64

Simplify the given expression. $$ 3^{2}-1^{2} $$

Short Answer

Expert verified
The simplified expression is 8.

Step by step solution

01

Simplify Powers in the Expression

Begin by evaluating the powers in the expression. Calculate each base raised to the power: \(3^2 = 9\) and \(1^2 = 1\). The expression simplifies to \(9 - 1\).
02

Perform Subtraction

Subtract the results of the powers obtained in Step 1. The expression becomes \(9 - 1 = 8\). Thus, the simplified expression is 8.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Understanding Powers
When we refer to powers in mathematics, we are talking about expressions that involve a base raised to an exponent. The base is the number being multiplied, while the exponent tells us how many times the base is used in the multiplication.
For instance, in the expression \(3^2\), "3" is the base and "2" is the exponent. This means that 3 is multiplied by itself once more鈥攁s in \(3 \times 3\)鈥攔esulting in 9. Let's consider another example: \(1^2\). Here "1" is the base and "2" is the exponent, which results in \(1 \times 1 = 1\).
  • The calculation for \(3^2\) represents multiplying 3 by itself once: \(3 \times 3 = 9\).
  • Similarly, \(1^2\) results in multiplying 1 by itself: \(1 \times 1 = 1\).
Understanding and evaluating the powers is the first step to simplifying expressions involving exponents, as seen in the original problem.
Performing Subtraction
Once we have evaluated the powers in the expression, the next step involves performing the subtraction operation. Subtraction is one of the basic operations in mathematics, where we find the difference between two numbers.
In our example, the expression simplified to 9 and 1 after calculating the powers. We perform subtraction by taking the second number away from the first. Therefore, we calculate:\[9 - 1 = 8\]
  • Start with the result from the first power calculation: 9.
  • Subtract the result from the second power calculation: 1 from 9.
  • This gives you the final result of 8.
Subtraction is straightforward, but it's important to check your work for accuracy to ensure you subtract correctly.
Simplification of the Expression
Simplification in mathematics involves reducing an expression to its simplest form. This means performing all possible operations such that no further simplification is needed.In the problem given, the expression \(3^2 - 1^2\) begins with two operations: calculating powers and then subtracting. The simplification process handles each of these in sequence.
The initial expression is simplified by:
  • First, reducing \(3^2\) to 9.
  • Then, reducing \(1^2\) to 1.
  • Finally, performing subtraction: \(9 - 1\).
Through simplification, the expression is reduced to the final answer, 8. Simplifying expressions makes them easier to work with and understand. It is a crucial skill when solving algebraic expressions and ensures mathematical problems are easier to manage.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

$$ 4+9 \cdot[7+6 \cdot(3+3)] $$$$ 15-1[19-(7+3)] $$

Simplify the given expression. $$ \frac{7+1}{8-4} $$

Simplify the given expression. $$ 4 \cdot\\{8+7\\} \div 3 $$

Simplify the given expression. $$ 15-5+10 $$

Simplify the given expression. $$ 3\\{8[6+5]-8[7+3]\\} $$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.