/*! 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 108 Simplify each exponential expres... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 108

Simplify each exponential expression. Assume that variables represent nonzero real numbers. $$\frac{\left(x y^{-2}\right)^{-2}}{\left(x^{-2} y\right)^{-3}}$$

Short Answer

Expert verified
The simplified expression for the given problem is \(x^{-8}y^{7}\)

Step by step solution

01

Expand using exponents rules

The given expression: \(\frac{(xy^{-2})^{-2}}{(x^{-2}y)^{-3}}\). Now we'll use power of power rule (a^{m^n} -> a^{m*n}), which states that to raise a power to a power, just multiply the exponents. Also remember that a^{-n} = 1/a^n. This expands to: \(\frac{x^{-2}*y^4}{x^6*y^{-3}}\)
02

Separate terms

Separate the terms in fraction: \(x^{-2}/x^6 * y^4/y^{-3}\)
03

Simplify terms using exponents rules

Using the rule which states that while dividing exponential terms with the same base, subtract the exponent at the bottom from the exponent at the top (a^m/a^n -> a^{m-n}), simplification leads to: \(x^{(-2-6)} * y^{(4-(-3))}\)
04

Simplify further

Calculating the expressions in the brackets gives: \(x^{-8}y^{7}\)

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

Determine whether each statement in Exercises 43鈥�50 is true or false. $$-13<-5$$

Suppose that a polynomial contains four terms. Explain how to use factoring by grouping to factor the polynomial.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The cube root of \(-8\) is not a real number.

Find the intersection of the sets. $$\\{1,3,7\\} \cap(2,3,8)$$

$$\frac{5}{4} \cdot \frac{8}{15}$$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

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.