/*! 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 155 Simplify each expression. $$\l... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 155

Simplify each expression. $$\left(\frac{2}{3} x^{2} y\right)^{3}$$

Short Answer

Expert verified
\( \frac{8}{27} x^6 y^3 \)

Step by step solution

01

Understand the Power Rule

The power rule states that \( (a^m)^n = a^{mn} \). Apply this rule to each part of the expression separately.
02

Distribute the Exponent

Apply the exponent of 3 to each part of the expression inside the parentheses: \( \left( \frac{2}{3} x^2 y \right)^3 = \left( \frac{2}{3} \right)^3 (x^2)^3 y^3 \).
03

Simplify the Fraction

Calculate \( \left( \frac{2}{3} \right)^3 \), which is \( \frac{2^3}{3^3} = \frac{8}{27} \).
04

Apply Exponent to Variables

Raise each variable to the power of 3: \( (x^2)^3 = x^{2 \times 3} = x^6 \) and \( y^3 \).
05

Combine Terms

Combine all parts to get the simplified expression: \( \frac{8}{27} x^6 y^3 \).

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Power Rule
The power rule is an essential concept in algebra. It helps us handle expressions where an exponent is raised to yet another exponent. The rule states that ewline When applying the power rule, it's crucial to remember that both the numerator and the denominator need to be raised to the power separately. Consider the expression This way, we ensure that we distribute the exponent correctly and simplify the expression accurately.
Exponents
Exponents are a shorthand way of expressing repeated multiplication of a number. For example, ewline The laws of exponents are helpful when simplifying algebraic expressions. For instance, when we have Remember, exponents can also apply to variables. By understanding these basic rules, we can handle more complex expressions with ease.
Fraction Simplification
Simplifying fractions involves reducing them to their simplest form. When dealing with fractions raised to a power, each part of the fraction (numerator and denominator) must be raised separately. Consider the step where we raised Simplification like this helps us get a cleaner, more understandable result. Always break down each part individually before combining them for the final expression.
Variable Exponentiation
Variable exponentiation involves raising variables to a specific power. When applying this, make sure to multiply the exponents. For instance, in the expression ewline The key is to manage each variable as its own entity and then combine the results for the final simplified expression. This technique provides structure and clarity when dealing with more complex algebraic expressions.

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

Mixed Practice $$\frac{32 y^{5}}{8 y^{2}}-\frac{60 y^{10}}{5 y^{7}}$$

Divide each polynomial by the binomial. $$\left(z^{3}+1\right) \div(z+1)$$

Divide each polynomial by the monomial. $$\left(48 y^{4}-24 y^{3}\right) \div\left(-8 y^{2}\right)$$

Divide each polynomial by the monomial. $$\frac{310 y^{4}-200 y^{3}}{5 y^{2}}$$

Divide each polynomial by the binomial. $$\left(a^{2}-2 a-35\right) \div(a+5)$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Statistics

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.