/*! 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 4 Write each of the following usin... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 4

Write each of the following using exponents. \(8 x x x y z z z z z\)

Short Answer

Expert verified
Question: Rewrite the expression \(8 x x x y z z z z z\) using exponents. Answer: \(8x^3y^1z^5\) or \(8x^3yz^5\)

Step by step solution

01

Identify the repeated bases with their counts

In the expression \(8 x x x y z z z z z\), we have the following bases repeated: - The number 8 appears only once. - The variable x appears three times. - The variable y appears only once. - The variable z appears five times.
02

Rewrite the expression using exponents

Now that we know the counts of each base, we can rewrite the expression using exponents: \(8x^3y^1z^5\)
03

Simplify the expression (if necessary)

In this case, there's no need to simplify further, as the exponents are already in the simplest form. Therefore, our final answer is: \(8x^3y^1z^5\) Note that since the exponent of y is 1, it's also correct to write the final answer as \(8x^3yz^5\).

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.

Algebraic Expressions
Algebraic expressions are combinations of numbers, variables, and arithmetic operations like addition, subtraction, multiplication, and division. In algebra, these expressions are used to describe mathematical relationships and solve problems involving unknown values. Let's break down these important components:
  • Numbers: These can be integers, fractions, or decimals, such as 8 in the example.
  • Variables: Symbols, often letters, that represent unknown quantities. In the exercise, x, y, and z are variables.
  • Operations: The actions performed on numbers and variables, including multiplication and other basic operations.
Understanding algebraic expressions allows you to simplify and manipulate them into forms that are easier to use in equations or to evaluate for specific values. In our example, transitioning the expression to a form with exponents gives us a version that鈥檚 neater and more convenient for further mathematical operations.
Mathematical Notation
Mathematical notation is a writing system that uses symbols and characters to represent numbers and operations, forming expressions and equations. It鈥檚 like the alphabet of mathematics, designed to express complex ideas concisely and clearly. An essential part of this notation involves the use of exponents.
  • Exponents: Used to show repeated multiplication of the same number. For instance, z appearing five times is written as \( z^5 \), meaning z multiplied by itself five times.
  • Base and Exponent: The base is the number being multiplied, while the exponent indicates how many times to multiply it. In \( x^3 \), x is the base, and 3 is the exponent.
By using exponents, the expression becomes much less cluttered and easier to work with, especially in more complex algebraic expressions. This helps in recognizing patterns and simplifies calculations in algebra.
Simplification of Expressions
Simplification is the process of transforming an expression into its simplest form. This means ensuring there's no unnecessary complexity, making it cleaner and easier to understand or use. In the solution provided, the expression was simplified using the rules of exponents.
  • Identify Repetitions: Recognize how many times each variable appears. This helps in rewriting the expression using exponents, as was done with \( x^3 \) and \( z^5 \).
  • Apply Exponent Rules: Use the repeated multiplication concept to reduce repetitive factors to a single term with an exponent. This not only simplifies the expression but also reduces risks of errors in further calculations.
  • Simplification Results: While expressions can look complex initially, like \( 8xxxyzzzzz \) did, converting to \( 8x^3y^1z^5 \) and dropping the \( y^1 \) (since any number to the power of 1 is itself) gives \( 8x^3yz^5 \), which is simpler and more straightforward to handle in algebraic tasks.

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

For the following problems, what integers can replace \(x\) so that the statements are true? $$ -3

Simplify the following problems. $$ \frac{u^{w}}{u^{k}} $$

Simplify the following problems. $$ x^{4} \cdot \frac{x^{10}}{x^{3}} $$

Simplify the following problems. $$ 1^{8}+0^{10}+3^{2}\left(4^{2}+2^{3}\right) $$

Simplify the following problems. $$ \left(a^{2 n} b^{3 m} c^{4 p}\right)^{6 r} $$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Calculus

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.