/*! 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 83 Simplify. \(\left[13 \div(20-7... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 83

Simplify. \(\left[13 \div(20-7)+2^{5}\right]-(2+3)^{2}\)

Short Answer

Expert verified
The expression simplifies to 8.

Step by step solution

01

Simplify inside Parentheses

Start by simplifying the expressions inside the parentheses. For the expression \((20-7)\), subtract 7 from 20 to get 13. For \((2+3)\), add 2 and 3 to get 5.
02

Substitute Simplified Expressions

Replace the parentheses with their simplified results. The expression now becomes \( rac{13}{13} + 2^{5} - 5^{2}\).
03

Division and Power of 2

Perform the division and calculate the power. \(\frac{13}{13} = 1\). Then calculate \(2^{5} = 32\). The expression is now \(1 + 32 - 5^{2}\).
04

Power of 5

Calculate the power of 5. \(5^{2} = 25\). The expression becomes \(1 + 32 - 25\).
05

Addition and Subtraction

Perform the addition and subtraction from left to right. First add: \(1 + 32 = 33\). Then subtract: \(33 - 25 = 8\).

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.

Arithmetic Expressions
Arithmetic expressions are mathematical statements that involve numbers and the four basic operations: addition, subtraction, multiplication, and division. These expressions can also include variables, exponents, and parentheses. Understanding how to interpret and solve these expressions is crucial for math proficiency.

Let's break it down further:
  • Numbers: The core components that are manipulated using arithmetic operations.
  • Operations: The processes applied to numbers, such as addition (+), subtraction (-), multiplication (脳), and division (梅).
  • Variables and Constants: While not seen in our example, these are symbols representing numbers.
  • Order of Operations: A set of rules that dictate the sequence in which operations are performed within an expression.
For our specific example, recognizing and ordering these operations correctly is key to simplifying the expression correctly.
Simplifying Expressions
Simplifying an expression involves performing all possible operations to reduce it to its simplest form. This often involves employing the order of operations rule, commonly remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

Here's how it applies:
  • Parentheses: First, solve any operations inside parentheses.
  • Exponents: Next, calculate any exponents (powers and roots).
  • Multiplication and Division: Work from left to right on these operations.
  • Addition and Subtraction: Finally, perform additions or subtractions, also from left to right.
This systematic approach allows us to consistently reach the correct simplified form of a complex expression.
Exponents
Exponents are shorthand for repeated multiplication of the same number. For example, in the expression \[2^{5}\], the notation "5" is the exponent, indicating that the number 2 should be multiplied by itself five times: \[2 \times 2 \times 2 \times 2 \times 2 = 32\].

Some important points about exponents include:
  • They are crucial for simplifying expressions and solving equations.
  • Knowing common exponent rules can simplify and speed up calculations, such as \[x^{a} \times x^{b} = x^{a+b}\].
In our problem, understanding that \[2^{5}\] is simply one number (32) helps streamline the reduction of the expression.
Parentheses in Math
Parentheses are essential in mathematics because they dictate the order in which calculations are performed. They group parts of an equation to explicitly prioritize them over others, ensuring consistency in mathematical interpretation and results.

In our example expression, parentheses are used to:
  • Group operations like \[(20-7)\], necessitating this operation be performed first to yield 13.
  • Combine numbers in operations such as \[(2+3)\], simplifying it to 5.
This helps prevent errors by clearly defining which calculations should take precedence based on their grouping. Correctly simplifying within parentheses before dealing with other operations is crucial for achieving the right answer.

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

The local college library is having a Million Pages of Reading promotion. The freshmen have read a total of 289,462 pages; the sophomores have read a total of 369,477 pages; the juniors have read a total of 218,287 pages; and the seniors have read a total of 121,685 pages. Have they reached the goal of one million pages? If not, how many more pages need to be read?

Check each addition below. If it is incorrect, find the correct answer. $$ \begin{array}{r} 566 \\ 932 \\ +\quad 871 \\ \hline 2369 \end{array} $$

The following table shows the top five automakers and the amount of money they spent on U.S. television advertising during a recent year. Use this table to answer Exercises 111 and 112. (Source: Automotive News) $$\begin{array}{|l|c|}\hline & \begin{array}{c}\text { Amount Spent on Television } \\\\\text { Advertising During a Recent Year }\end{array} \\\\\hline \text { General Motors } & \$ 3,500,000,000 \\\\\hline \text { Ford } & \$ 2,680,000,000 \\\\\hline \text { Fiat Chrysler Automobiles } & \$ 2,250,000,000 \\\\\hline \text { Toyota } & \$ 1,800,000,000 \\\\\hline \text { Nissan } & \$ 1,140,000,000 \\\\\hline\end{array}$$ Find the average amount of money spent on television ads by the top two advertisers.

Explain why the phrase "Subtract 7 from 10 " translates to \(" 10-7 . "\)

On August 23,1989 , it was estimated that 1,500,000 people joined hands in a human chain stretching 370 miles to protest the fiftieth anniversary of the pact that allowed what was then the Soviet Union to annex the Baltic nations in \(1939 .\) If the estimate of the number of people is to the nearest hundredthousand, determine the largest possible number of people in the chain.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

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.