Problem 45 Simplify. $$-10^{3}$$... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

1 Edition

Chapter 2: Problem 45

Simplify. $$-10^{3}$$

Short Answer

Expert verified

-1000

Step by step solution

Understand the Expression

The expression offers the negative sign followed by a number which raised to the exponent 3. This is important to distinguish from the negative number itself being raised to the power.

Apply the Exponentiation

Calculate the value of (10^3). Recall that exponentiation means multiplying the base number, 10, by itself the number of times indicated by the exponent, which in this case is 3.So, 10^3 = 10 脳 10 脳 10 = 1000.

Apply the Negative Sign

Since the negative sign is outside the exponent, it should be applied after the exponentiation is completed. Therefore, offers becomes -1000.

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Key Concepts

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

Negative Exponents

When working with exponents, you might encounter negative exponents. A negative exponent indicates that the base should be taken as the reciprocal and then raised to the absolute value of the exponent. For example, $10^{-3}$ means we should take the reciprocal of 10, which is $\frac{1}{10}$, and raise it to the power of 3. So, $10^{-3}$ is the same as $\frac{1}{10^3}$ or $\frac{1}{1000}$. Understanding negative exponents is crucial in simplifying exponential expressions, especially in algebra. Remember:
- A negative exponent turns the base into its reciprocal.
- Then, raise the reciprocal to the positive of the exponent.

Order of Operations

To solve any mathematical expression correctly, you must follow the order of operations. This is often remembered by the acronym PEMDAS, which stands for:

Parentheses
Exponents
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)

The order of operations ensures that expressions are simplified in a consistent manner. For example, in the expression $-10^3$, exponentiation comes before applying the negative sign. This means you first calculate $10^3$ and then apply the negative sign, resulting in -1000. Ignoring the order of operations can lead to incorrect results.

Powers of Ten

Powers of ten are a fundamental concept in mathematics and make calculations easier to manage. When you raise 10 to any exponent, you are simply moving the decimal point to the right by the number of places equal to that exponent.
For example:

$10^1 = 10$
$10^2 = 100$
$10^3 = 1000$

Each step increases the value by a factor of ten. This concept is particularly useful in scientific notation, where large or small numbers are expressed in terms of powers of ten. For instance, the number 1000 can be written as $10^3$, making it easier to read and compare with other numbers expressed similarly.

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91影视

Simplify. $$-10^{3}$$

Short Answer

Step by step solution

Understand the Expression

Apply the Exponentiation

Apply the Negative Sign

Key Concepts

Negative Exponents

Order of Operations

Powers of Ten

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