/*! 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 12 Express using positive exponents... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 12

Express using positive exponents and, if possible, simplify. $$10^{-4}$$

Short Answer

Expert verified
\(10^{-4} = \frac{1}{10^4}\)\

Step by step solution

01

- Understand Negative Exponent Rule

Recall the rule for negative exponents: If you have a term with a negative exponent, such as \(a^{-n}\), it can be rewritten as \(\frac{1}{a^n}\).
02

- Apply Negative Exponent Rule

Apply the negative exponent rule to the given term \(10^{-4}\). This becomes \(\frac{1}{10^4}\).

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.

Negative Exponent Rule
When dealing with exponents, remember that a negative exponent indicates division. It essentially means that the base should be on the other side of a fraction. For instance, a term like \(a^{-n}\) can be expressed as \(\frac{1}{a^n}\). This rule helps in converting negative exponents into a more familiar form with positive exponents.
Let's take an example: if you have \(5^{-3}\), according to the negative exponent rule, you can rewrite it as \(\frac{1}{5^3}\). Hence, understanding this rule is crucial in simplifying expressions with negative exponents.
Simplification
Simplification involves reducing an expression to its simplest form. By applying the negative exponent rule, we can simplify terms easily. For example, if you come across \(10^{-4}\), you use the negative exponent rule to make it into \(\frac{1}{10^4}\).
This process is critical in algebra, as it reduces complexity and makes it easier to handle further calculations. Always look for ways to simplify terms by applying known mathematical rules, ensuring that the expression is as straightforward as possible.
Positive Exponents
Positive exponents are perhaps what most students are familiar with when they first learn about exponents. A positive exponent indicates how many times the base is multiplied by itself. For example, in the term \(10^4\), the '4' means that 10 is multiplied by itself four times: \(10 \times 10 \times 10 \times 10 = 10000\).
After converting a negative exponent into a positive one using the negative exponent rule, you can easily interpret and simplify the term. In our exercise, after we converted \(10^{-4}\) to \(\frac{1}{10^4}\), it became clear that we are dealing with a positive exponent in the denominator.
Algebraic Expressions
Algebraic expressions can include numbers, variables, and exponents, combined using arithmetic operations. Understanding how to manipulate these expressions is fundamental in algebra.
When working with expressions involving exponents, it's important to apply rules like the negative exponent rule correctly. Consider the initial exercise term \(10^{-4}\). By converting it using the negative exponent rule (becoming \(\frac{1}{10^4}\)), we simplify its appearance and make it easier to work with. Recognizing and correctly applying such rules ensures that we can handle more complex algebraic expressions with confidence.

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

For each pair of functions fand \(g\), determine the domain of the sum, the difference, and the product of the two functions. $$ \begin{aligned} &f(x)=\frac{5}{3-x}\\\ &g(x)=\frac{x}{4 x-1} \end{aligned} $$

Simplify. Assume that no denominator is zero and that \(0^{0}\) is not considered. $$ \left(\frac{5 a^{7}}{2 b^{5} c}\right)^{0} $$

Find the domain of \(F / G,\) if $$ F(x)=\frac{1}{x-4} \quad \text { and } \quad G(x)=\frac{x^{2}-4}{x-3} $$

In computer science, \(1 \mathrm{KB}\) of memory refers to 1 kilobyte, or 1 \(\times 10^{3}\) bytes, of memory. This is really an approximation of 1 \(\times 2^{10}\) bytes (since computer memory uses powers of \(2)\). The TI- 84 Plus Silver Edition graphing calculator has \(1.5 \mathrm{MB}\) (megabytes) of FLASH ROM, where \(1 \mathrm{MB}\) is \(1000 \mathrm{KB}\). How many bytes of FLASH ROM does this calculator have?

Simplify. Assume that no denominator is zero and that \(0^{0}\) is not considered. $$ \left(\frac{x^{2} y}{z^{3}}\right)^{4} $$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Pure 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.