/*! 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 44 \(5 \times 10^{4}-2 \times 10^{4... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 44

\(5 \times 10^{4}-2 \times 10^{4}\)

Short Answer

Expert verified
30000

Step by step solution

01

Identify the components

Separate and identify the components of the expression: 1. The first term: \( 5 \times 10^{4} \) 2. The second term: \( 2 \times 10^{4} \)
02

Simplify each term

Recognize that both terms have the same base of 10 raised to the power of 4. Thus, simplify each term with this understanding: 1. The first term: \( 5 \times 10^{4} = 50000 \) 2. The second term: \( 2 \times 10^{4} = 20000 \)
03

Subtract the simplified terms

Subtract the second term from the first term:\( 50000 - 20000 = 30000 \)

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.

scientific notation
Scientific notation is a way of writing very large or very small numbers in a compact form using powers of ten. This is particularly useful in mathematics and science.
A number in scientific notation is expressed as the product of a number between 1 and 10 and a power of ten. For example, the number 50,000 can be written in scientific notation as \[ 5 \times 10^{4} \].
The notation consists of:
  • A coefficient (a number between 1 and 10).
  • A base of 10 raised to an exponent.
In the exercise above,\ \[ 5 \times 10^{4} \] \ and \ \[ 2 \times 10^{4} \] are in scientific notation because they follow this structure.
Changing these terms back to standard form (decimal form) can make subtraction or addition easier.
That's what we did in step 2 of the solution.
subtraction of like terms
Subtraction of like terms refers to subtracting numbers or expressions that have the same variables and powers.

Similar to grouping together similar items, like terms in algebra can be easily operated upon.
The exercise above uses like terms, so we can simplify and subtract them directly.

Both terms, \ 5\times10^{4} \ and \ 2\times 10^{4}, \ share the same base \({10}\) raised to the same power (\({4}\)).
This makes them perfect candidates for subtraction.
We simplify to:
  • \({50000 - 20000 = 30000}\)
By converting the terms to standard form, the subtraction is straightforward.
basic algebra steps
Basic algebra involves a series of fundamental steps to solve problems. Here, we break down the process:

In the given exercise, the steps were:
  • Identify and separate the components.
  • Simplify each term (in standard form).
  • Subtract the simplified terms.
Identifying components is crucial for understanding what you are working with. Next, simplifying terms helps make complex expressions more manageable.
Finally, performing the basic operation (like subtraction) yields the solution.

By following these basic steps, algebraic expressions become easier to solve. Whether the problem involves scientific notation, like terms, or any other algebraic concept, these steps create a solid framework for solutions.

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

\(\left(c^{2}+8\right) \div(c+6)\)

\(\left(x^{2}-100\right) \div(x+10)\)

\(\left(12 a^{4}+6 a^{3}-3 a^{2}\right) \div 3\)

\(\left(54 z^{4}-36 z^{3}-6 z^{2}+12 z\right) \div(6 z)\)

\(\left(5 w^{4}-15 w^{2}+60 w+20\right) \div(5 w)\)
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Mechanics 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.