/*! 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 58 Simplify. $$ 40-3^{2}-2^{3} ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 58

Simplify. $$ 40-3^{2}-2^{3} $$

Short Answer

Expert verified
The simplified expression is 23.

Step by step solution

01

Evaluate the exponents

First, calculate the value of the exponents. Begin with evaluating the term \(3^{2}\). This equals \(3 \times 3 = 9\). Next, evaluate \(2^{3}\). This equals \(2 \times 2 \times 2 = 8\).
02

Substitute the evaluated exponents back into the expression

Now, substitute the evaluated terms back into the original expression. This gives us \(40 - 9 - 8\).
03

Perform the subtraction

Subtract the evaluated terms sequentially from the initial value. Start with \(40 - 9 = 31\), and then subtract \(8\) from \(31\). This equals \(31 - 8 = 23\).

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.

evaluating exponents
To solve algebraic expressions effectively, we need to understand and evaluate exponents. Exponents denote how many times a number (the base) is multiplied by itself. For example, in the term \(3^{2}\), the base is 3, and the exponent is 2. This means we multiply 3 by itself: \(3 \times 3\) which equals 9. When we see \(2^{3}\), it means \(2 \times 2 \times 2\), which totals 8.
Evaluating exponents is typically the first step in simplifying expressions as per the order of operations.
order of operations
The order of operations is fundamental in algebra, ensuring that everyone solves an expression the same way. The shorthand for remembering this order is PEMDAS:
  • P: Parentheses first
  • E: Exponents (powers and roots, etc.)
  • M and D: Multiplication and Division (left to right)
  • A and S: Addition and Subtraction (left to right)
In the expression \(40 - 3^{2} - 2^{3}\), after evaluating the exponents (which we did to get 9 and 8), the next steps follow the sequence of subtraction from left to right. Thus, after substitution, we perform \(40 - 9 = 31\), followed by \(31 - 8 = 23\).
subtraction
Subtraction is one of the basic arithmetic operations where we remove a number from another. Unlike addition, subtraction isn't commutative; the order matters. In our problem, we simplified \(40 - 9 - 8\). It's important to subtract in sequence: first, subtract 9 from 40, yielding 31, then subtract 8, yielding 23.
Remember that subtraction reduces the quantity of the initial number, and checking the order ensures accuracy in results.

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

Simplify. $$ (8-7)-9 $$

Divide. $$ -\frac{5}{9} \div\left(-\frac{5}{6}\right) $$

Solve. Bank Account Balance. Karen had \(\$ 234\) in her bank account. After she used her debit card to make seven purchases at \(\$ 39\) each, what was the balance in her bank account?

Simplify. $$ 10(-5)+1(-1) $$

Simplify. $$ -1000 \div(-100) \div 10 $$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

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.