Problem 77 Simplify. $$ 2 \times 10^{3}... [FREE SOLUTION]

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Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 10: Problem 77

Simplify. $$ 2 \times 10^{3}-5000 $$

Short Answer

Expert verified

The answer is $-3000$.

Step by step solution

Understand the problem

The problem requires simplifying the expression: $2 \times 10^{3} - 5000$.

Calculate the exponent

First, calculate $2 \times 10^{3}$. This means multiplying 2 by 1000 since $10^{3} = 1000$. Therefore, $2 \times 1000 = 2000$.

Perform the subtraction

Now subtract 5000 from 2000. Calculate: $2000 - 5000 = -3000$.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Exponentiation

Exponentiation is a core concept in algebra and mathematics in general. It involves raising a number (called the base) to the power of an exponent. For example, in the expression $10^{3}$, the base is 10 and the exponent is 3.
This means you multiply the base by itself as many times as the exponent indicates:

$10^{3} = 10 \times 10 \times 10 = 1000$

In this specific problem, we used exponentiation to transform $10^{3}$ into 1000, making the calculation simpler.
This step is crucial because it allows us to convert complex expressions into more manageable forms.
By understanding exponentiation, you're better prepared for simplifying and solving various mathematical problems.

Subtraction

Subtraction is one of the basic operations in arithmetic and algebra. It involves taking one number away from another. For example, in the expression $2000 - 5000$, the number 5000 is subtracted from 2000.
This operation determines the difference between the two numbers.
In our specific problem, we simplified the expression first by calculating the exponent. This step resulted in the simpler expression $2000 - 5000$.
When you subtract a larger number from a smaller one, like the case here, the result will be a negative number:

$2000 - 5000 = -3000$

Understanding subtraction helps in solving equations and simplifying expressions effectively.

Basic Algebra

Basic algebra involves understanding and manipulating mathematical symbols and expressions to solve problems. In this exercise, we demonstrated the following concepts:

Exponentiation: We calculated $2 \times 10^{3}$ by converting $10^{3}$ to 1000 and then multiplying by 2 to get 2000.
Subtraction: We then subtracted 5000 from 2000 to get the final answer, -3000.

Using these fundamental processes, we simplified a potentially complex expression into an understandable form.
This is a simple yet powerful example of how basic algebra can be used to break down and solve problems efficiently.
Mastering basic algebra lays the foundation for more advanced mathematical concepts.

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91影视

Simplify. $$ 2 \times 10^{3}-5000 $$

Short Answer

Step by step solution

Understand the problem

Calculate the exponent

Perform the subtraction

Key Concepts

Exponentiation

Subtraction

Basic Algebra

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