Problem 34 Divide as indicated. Write your ... [FREE SOLUTION]

91影视

Prealgebra

Charles P. McKeague

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 9: Problem 34

Divide as indicated. Write your answer using only positive exponents. $$\frac{X^{5}}{X^{7}}$$

Short Answer

Expert verified

$\frac{1}{X^2}$

Step by step solution

Apply Exponent Division Rule

When dividing exponential expressions with the same base, we subtract the exponent of the denominator from the exponent of the numerator: $\frac{X^5}{X^7} = X^{5-7} = X^{-2}$.

Convert to Positive Exponents

To express the answer using only positive exponents, recall that $X^{-a} = \frac{1}{X^a}$. So, we convert $X^{-2}$ to positive exponents:\[ X^{-2} = \frac{1}{X^2}. \]

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.

Exponent Rules

Exponent rules might seem complicated at first, but they are super helpful in simplifying expressions. The main rule used in this exercise is the division of exponents when the bases are the same. When you have two powers with the same base, like $ \frac{X^m}{X^n} $, the rule is to subtract the exponents:

Keep the base the same.
Subtract the exponent in the denominator from the exponent in the numerator, so it becomes $ X^{m-n} $.

This method allows us to simplify expressions, making them much easier to work with. So remember, when you are dividing powers, focus on the exponents, not the base itself.

Positive Exponents

Positive exponents are a super friendly way of expressing numbers. Instead of dealing with negative powers, we can transform them into their positive counterpart. This is especially useful in math problems as it often makes interpretation easier. For any base $ X $ raised to a negative exponent, such as $ X^{-a} $, you convert it to a positive exponent using this rule:

Take the reciprocal of the base with a positive exponent: $ X^{-a} = \frac{1}{X^a} $.

By doing this, the expression becomes positive and often simpler, which makes calculations more straightforward in many cases.

Division of Powers

Dividing powers involves more than just applying one rule; it's about seeing the relationship between similar exponential terms. When you divide two expressions with the same base, the important task lies in handling the exponents correctly.

The base remains unchanged when dividing.
The exponent in the numerator is subtracted by the exponent in the denominator.

For instance, in $ \frac{X^5}{X^7} $, you subtract 7 from 5, resulting in $ X^{-2} $. After applying the rule, if the resulting exponent is negative, you can easily convert it to its positive form, as explained in the previous section. Understanding this gives you a powerful tool for simplifying expressions efficiently.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Divide as indicated. Write your answer using only positive exponents. $$\frac{X^{5}}{X^{7}}$$

Short Answer

Step by step solution

Apply Exponent Division Rule

Convert to Positive Exponents

Key Concepts

Exponent Rules

Positive Exponents

Division of Powers

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Theoretical and Mathematical Physics

Probability and Statistics

Statistics

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.