/*! 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 71 Find the value of each expressio... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 71

Find the value of each expression $$\left[\left(\frac{2}{3}\right)^{2}-\frac{1}{3}\right]^{2}$$

Short Answer

Expert verified
So, the value of the given expression is \(\frac{1}{81}\).

Step by step solution

01

Deal With the Operations Inside the Parentheses

First, calculate the square of \(\frac{2}{3}\), which gives \(\frac{4}{9}\). So, our expression becomes: \(\left[\frac{4}{9}-\frac{1}{3}\right]^{2}\).
02

Subtraction in the Brackets

Next, subtract \(\frac{1}{3}\) from \(\frac{4}{9}\). But to subtract these two fractions, they need to have the same denominator. The least common denominator (LCD) for 3 and 9 is 9, so change \(\frac{1}{3}\) to \(\frac{3}{9}\) (multiply the numerator and the denominator by 3). This gives \(\left[\frac{4}{9}-\frac{3}{9}\right]^{2}\), which simplifies to \(\left[\frac{1}{9}\right]^{2}\).
03

Square the Result

Now, square \(\frac{1}{9}\), which gives \(\frac{1}{81}\).

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

Explain how you would decide which of two decimal fractions is the larger.

Explain how to convert a mixed number into an improper fraction.

A woman earns \(\$ 48,712.32\) in taxable income. She must pay \(15 \%\) tax on the first 823,000 and \(28 \%\) on the rest. In addition, she must pay a Social Security tax of \(15.4 \%\) on the total amount. How much tax will she need to pay?

Wendy has \(x\) shares of stock. Her sister has 2 fewer shares than twice Wendy's shares. How many shares does her sister have?

Write each inequality as an equivalent inequality in which the inequality symbol points in the opposite direction. $$\frac{12}{4}<\frac{24}{6}$$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Geometry

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.