/*! 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 434 In the following exercises, simp... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 434

In the following exercises, simplify each expression. $$ 3^{2}-7^{2} $$

Short Answer

Expert verified
-40

Step by step solution

01

Identify the exponents

Recognize the bases and their respective exponents in the expression. Here, the terms are \(3^2\) and \(7^2\).
02

Calculate each power

Evaluate the exponents individually. Calculate \(3^2 = 3 \times 3 = 9\) and \(7^2 = 7 \times 7 = 49\).
03

Substitute back into the expression

Replace the original terms with their evaluated values: \(9 - 49\).
04

Perform the subtraction

Subtract the values: \(9 - 49 = -40\).

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.

Exponents
In mathematics, an exponent represents the number of times a base number is multiplied by itself. The expression is written as the base number followed by a superscript. For example, in the expression \(3^2\), 3 is the base and 2 is the exponent. This simply means that we multiply 3 by itself: \(3 \times 3 = 9\).
Exponents are a shorthand way to show repeated multiplication.
Here are some key points about exponents:
  • An exponent of 1 means the number remains the same: \(a^1 = a\)
  • An exponent of 0 means the number equals 1: \(a^0 = 1\)
  • Negative exponents represent division: \(a^{-n} = \frac{1}{a^n}\)
Understanding exponents helps in simplifying expressions easily.
Powers
Powers refer to expressions like \(a^n\), where a is the base and n is the exponent. It tells us how many times to multiply the base by itself. If we see \(7^2\), it means we multiply 7 by itself: \(7 \times 7 = 49\).
This concept plays a crucial role in dealing with mathematical expressions involving large numbers. For example:
  • \(2^3 = 2 \times 2 \times 2 = 8\)
  • \(5^4 = 5 \times 5 \times 5 \times 5 = 625\)
Calculating powers simplifies operations and makes it easier to work with exponential numbers. In our exercise case, calculating \(3^2\) and \(7^2\) separately before simplifying the expression was crucial.
Subtraction
Subtraction is one of the basic arithmetic operations. It denotes removing objects from a collection. Mathematically, it鈥檚 often shown with the minus symbol (\(-\)). For instance, in our expression \(9 - 49\), subtraction means taking 49 away from 9. This results in:
\(9 - 49 = -40\)
Subtraction becomes straightforward once the individual terms are simplified. Always ensure to:
  • Calculate individual terms or powers.
  • Replace the original terms with their evaluated values.
Following these steps carefully ensures accuracy in solving math problems involving subtraction and other operations.

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

In the following exercises, evaluate. $$ (-2 r)^{2} \text { when } r=3 $$

In the following exercises, solve the given applications. Temperature On January 4, the high temperature in Laredo, Texas was 78 degrees, and the high in Houlton, Maine was ?28 degrees. What was the difference in temperature of Laredo and Houlton?

In the following exercises, translate each of the following phrases into expressions with positive or negative numbers. a temperature of 10 below zero

In the following exercises, simplify each expression. $$ -3^{4} $$

In the following exercises, solve. $$ -9 r=-54 $$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

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.