/*! 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 27 Evaluate the expression. Write f... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 27

Evaluate the expression. Write fractions in simplest form. $$ \left(\frac{6}{2}\right)^{3} $$

Short Answer

Expert verified
The expression \((\frac{6}{2})^{3}\) simplifies to 27.

Step by step solution

01

Perform Division

First, execute the division inside the parentheses. \( \frac{6}{2} = 3 \). So, the revised expression is \(3^{3}\).
02

Apply Exponentiation

Now compute the expression \(3^{3}\). This is achieved by multiplying 3 by itself twice, as the exponent tells us how many times to multiply the base (3) by itself. Hence, \(3^{3} = 3 * 3 * 3 = 27\).
03

Simplify Result

The result, 27, cannot be further simplified as the exercise didn鈥檛 result in a fraction. Hence, the expression \((\frac{6}{2})^{3}\) evaluates to 27.

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.

Simplify Fractions
Fractions can feel tricky at first, but simplifying them makes them easier to work with. A fraction is in its simplest form when the numerator (top number) and the denominator (bottom number) have no common divisors other than 1. To simplify a fraction:
  • Identify the greatest common factor (GCF) for both the numerator and the denominator.
  • Divide both the top and the bottom by this GCF.
In the expression \[\left(\frac{6}{2}\right)\]the GCF of 6 and 2 is 2. By dividing both 6 and 2 by their GCF:
  • \[\frac{6}{2} = \frac{3}{1}\]
This gives us the simplest form, which is 3. Simplifying fractions is about making them as straightforward as possible, so always check if the numbers can be divided by a common factor before you move on to further calculations.
Division
Division is one of the four basic operations in arithmetic. It involves splitting a number into equal parts or groups. In mathematical expressions, division shows how many times one number is contained within another. Consider the example provided:\[\left(\frac{6}{2}\right)\]When you perform division here, you're finding out how many times 2 goes into 6.
  • 6 divided by 2 equals 3 because when 2 is multiplied by 3, it returns to 6.
Division uses the symbol "/" or a fraction bar, and understanding it is crucial for properly managing mathematical problems that include dividing quantities. Practicing with simple numbers, like dividing 6 by 2, builds confidence for more complex math operations.
Order of Operations
The order of operations is essential for tackling any mathematical expression correctly. It dictates the sequence in which you should solve parts of an expression. The common acronym PEMDAS can help you remember:
  • Parentheses
  • Exponents
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)
Let's break down the expression \[\left(\frac{6}{2}\right)^3\]Following PEMDAS:
  • Do the operations inside the parentheses first; here, it鈥檚 the division \[\frac{6}{2} = 3\].
  • Next, deal with the exponent, calculated as \[3^3 = 3 \times 3 \times 3 = 27\].
Adhering to this order avoids mistakes, especially in long and complex expressions. Without it, calculations might yield incorrect results, so always keep PEMDAS in mind!

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

Write your answer as a power or as a product of powers. $$ \left(a b c^{2}\right)^{3}\left(a^{2} b\right)^{2} $$

Write your answer as a power or as a product of powers. $$ 2 x^{3} \cdot(3 x)^{2} $$

Solve the inequality. Then sketch a graph of the solution on a number line. $$|9-2 x|+3<4 \quad $$

Evaluate the expression. $$\left(\frac{1}{2}\right)^{3}$$

Write your answer as a power or as a product of powers. $$ (3 b)^{3} \cdot b $$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

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.