/*! 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 51 Simplify. $$ \frac{7000+(-10... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 15: Problem 51

Simplify. $$ \frac{7000+(-10)^{3}}{10^{2} \cdot(2+4)} $$

Short Answer

Expert verified
10

Step by step solution

01

Simplify the numerator

First, simplify the expression in the numerator. The numerator is given as \(7000 + (-10)^3\). Calculate \((-10)^3\) which is equal to \(-1000\). So, the numerator becomes \(7000 + (-1000)\), which simplifies to \(6000\).
02

Simplify the denominator

Next, simplify the expression in the denominator. The denominator is given as \(10^2 \cdot (2+4)\). Calculate \(10^2\) which is \(100\) and \(2+4\) which is \(6\). Therefore, the denominator is \(100 \cdot 6 = 600\).
03

Divide the simplified numerator by the simplified denominator

Now, divide the simplified numerator by the simplified denominator: \(\frac{6000}{600}\). This simplifies to \(10\).

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.

Numerator
The numerator is the top part of a fraction. In the problem above, the numerator is given as \(7000 + (-10)^3\). To solve it, you first need to calculate \((-10)^3\). Since multiplying three negative numbers results in a negative number, \((-10)^3 = -1000\). So, the numerator becomes \(7000 + (-1000) = 6000\). This means we have successfully simplified the numerator to 6000.
Denominator
The denominator is the bottom part of a fraction. In this problem, the denominator is \(10^2 \cdot (2+4)\). First, calculate \(10^2\). Raising 10 to the power of 2 (or squaring it) means multiplying 10 by itself: \(10^2 = 100\). Next, calculate \(2+4\). The sum is 6. Finally, multiply the two results: \(100 \cdot 6 = 600\). So, the simplified denominator is 600.
Exponents
Exponents are used to represent repeated multiplication of a number by itself. In the numerator, we see \((-10)^3\). This means we multiply -10 by itself three times: \((-10) \times (-10) \times (-10) = -1000\). In the denominator, we have \(10^2\), which means 10 multiplied by itself: \(10 \times 10 = 100\). Understanding exponents helps simplify numerical expressions significantly.
Arithmetic Operations
Simplifying algebraic expressions often involves several arithmetic operations: Addition, subtraction, multiplication, and division. In the example problem, we:
  • Calculated the power of numbers (exponents).
  • Added and subtracted numbers in the numerator, \( 7000 + (-1000) = 6000 \).
  • Performed addition inside the parentheses in the denominator, \( 2+4=6 \).
  • Multiplied results to get the simplified denominator, \( 10^2 \cdot 6 = 600 \).
  • Finally, divided the numerator by the denominator, giving us the simple result, \( 6000 / 600 = 10 \).
Grasping these operations is essential when solving complex algebraic expressions.

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

Factor. $$ 8 x+6 y $$

Simplify. $$ 25-8 \cdot 3+1 $$

Translate each problem to an equation. Do not solve. What number added to 256 is \(113 ?\)

Solve each system graphically. $$ \begin{array}{l} {y=\frac{1}{3} x+2} \\ {y=\frac{1}{3} x-7} \end{array} $$

Translate each problem to an equation. Do not solve. A McDonald's Big Mac contains 500 calories. This is 69 more calories than a Taco Bell Beef Burrito provides. How many calories are in a Taco Bell Beef Burrito?
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

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.