/*! 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 99 Simplify using properties of exp... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 99

Simplify using properties of exponents. $$\frac{\left(3 y^{\frac{1}{4}}\right)^{3}}{y^{\frac{1}{12}}}$$

Short Answer

Expert verified
The simplified form of \(\frac{(3 y^{1/4})^{3}}{y^{1/12}}\) is \(27 y^{2/3}\).

Step by step solution

01

Rewrite the power of a power expression

To simplify, the first step is to rewrite the power of a power expression on the numerator by multiplying the exponents. Given \((3 y^{1/4})^3\), apply the rule \(a^{m \cdot n} = (a^m)^n\) to get, \(3^3 y^{(1/4) \cdot 3} = 27 y^{3/4}\).
02

Subtract the exponents

The second step is to subtract the exponent of the denominator from the exponent of the numerator. Given \(27 y^{3/4} / y^{1/12}\), apply the rule \(a^{m}/a^{n} = a^{m-n}\) to get, \(27 y^{(3/4 - 1/12)}\).
03

Simplify the exponent

Convert both fractions to a common denominator and calculate the difference. From step 2, simplify the exponent of \(y\) in \(27 y^{(3/4 - 1/12)}\) to \(27 y^{(9/12 - 1/12) = 27 y^{8/12}}.\); this can be further simplified to \(27 y^{2/3}.\)

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

Simplify by reducing the index of the radical. $$\sqrt[6]{x^{4}}$$

Evaluate each expression without using a calculator. $$8^{\frac{2}{3}}$$

Find all integers b so that the trinomial can be factored. $$ x^{2}+b x+15 $$

How do you know if a number is written in scientific notation?

If \(b^{A}=M N, b^{C}=M,\) and \(b^{D}=N,\) what is the relationship among \(A, C,\) and \(D ?\)
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

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.