/*! 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 28 Simplify the given expression. ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 28

Simplify the given expression. $$ \frac{x^{-11}\left(y^{3}\right)^{-2}}{\left(x^{-3}\right)^{5}\left(y^{2}\right)^{4}} $$

Short Answer

Expert verified
The simplified expression is \(\frac{x^4}{y^{14}}\).

Step by step solution

01

- Apply the Power of a Power Rule

We will apply the power of a power rule, which states that \((a^m)^n = a^{mn}\). \[ \frac{x^{-11}(y^3)^{-2}}{(x^{-3})^5(y^2)^4} = \frac{x^{-11}y^{-6}}{x^{-15}y^8} \]
02

- Apply the Product of Powers Rule

Now we will apply the product of powers rule, which states that \(\frac{a^m}{a^n} = a^{m-n}\). \[ \frac{x^{-11}y^{-6}}{x^{-15}y^8} = x^{-11-(-15)}y^{-6-8} = x^4 y^{-14} \]
03

- Rewrite in Positive Exponent Form

Since the exponent of y is negative, we will rewrite it in positive exponent form. \[ x^4 y^{-14} = x^4 \cdot \left(\frac{1}{y^{14}}\right) = \frac{x^4}{y^{14}} \] The simplified expression is \(\frac{x^4}{y^{14}}\).

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!

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

Suppose \(q\) is a polynomial of degree 4 such that $$ \begin{array}{r} q(0)=-1 . \text { Define } p \text { by } \\ \qquad p(x)=x^{5}+q(x) . \end{array} $$ Explain why \(p\) has a zero on the interval \((0, \infty)\).

Explain why the composition of a polynomial and a rational function (in either order) is a rational function.

Write each expression as the sum of a polynomial and a rational function whose numerator has smaller degree than its denominator. $$ \frac{2 x+1}{x-3} $$

Write the domain of the given function \(r\) as a union of intervals. $$ r(x)=\frac{4 x^{7}+8 x^{2}-1}{x^{2}-2 x-6} $$

Suppose $$r(x)=\frac{x+1}{x^{2}+3} \quad \text { and } \quad s(x)=\frac{x+2}{x^{2}+5}$$ Find two distinct numbers \(x\) such that \(s(x)=\frac{1}{8}\).
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Decision 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.