/*! 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 17 In Exercises \(11-24\), use the ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 17

In Exercises \(11-24\), use the zero-exponent rule to simplify each expression. $$100 y^{0}$$

Short Answer

Expert verified
The simplified expression is 100.

Step by step solution

01

Identify the Zero Exponent

In the provided exercise, it can be noticed that y is raised to the power of 0. As the exercise instructs, the zero-exponent rule must be used to simplify this expression.
02

Apply the Zero Exponent Rule

The zero-exponent rule states that any non-zero number raised to the power of 0 is equal to 1. Applying this rule to the term \(y^0\), it can be deduced that \(y^0\) is equal to 1.
03

Simplify the Expression

Finally, replacing \(y^0\) with 1 in the original expression \(100y^0\), the expression can be simplified to \(100 * 1\), which equals to 100.

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.

Simplifying Expressions
Simplifying expressions in algebra is all about making them easier to read and understand. This often involves reducing complex expressions to simpler forms.
Think about it like cleaning up your room: you're arranging everything in its simplest and most straightforward form. In the given exercise, this meant using the zero exponent rule to reduce the term \( y^0 \) to a more manageable form.
By focusing on the zero exponent in the expression \( 100y^0 \), we make the seemingly complex simpler, which is a common goal when simplifying any algebraic expression.
Mathematical Rules
Mathematical rules are the foundations that help us solve and simplify problems. They provide us with formulas and principles that apply to a variety of situations, acting like a map that guides us through the terrain of numbers and operations.
The zero-exponent rule is an example of such a rule, stating simply that any non-zero number raised to the power of zero is equal to one.
  • This rule holds true regardless of the number itself, whether it's a small number like \(3\) or a variable like \(y\).
  • It鈥檚 a powerful tool for simplifying expressions and making calculations easier.
By knowing and applying mathematical rules effectively, we gain the ability to simplify even the most intimidating expressions with confidence.
Algebraic Expressions
Algebraic expressions are mathematical phrases that can include numbers, variables, and operations. They are the building blocks of algebra and can represent all kinds of real-world and abstract concepts.
Understanding algebraic expressions is crucial because they're used in equations and formulas to solve problems. For example, in the expression \( 100y^0 \), "100" is a coefficient and \(y^0\) represents a variable term raised to a power.
  • The process of simplifying an algebraic expression often involves identifying parts of the expression that can be reduced or changed according to mathematical rules.
  • These elements can include coefficients, variables, and exponents.
By mastering algebraic expressions, you can solve complex problems more intuitively and quickly.

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

Perform the indicated operations. $$(y+1)\left(y^{2}-y+1\right)-(y-1)\left(y^{2}+y+1\right)$$

In Exercises \(85-86,\) the variable \(n\) in each exponent represents a natural mumber. Divide the polynomial by the monomial. Then use polynomial multiplication to check the quotient. $$\frac{12 x^{15 n}-24 x^{12 n}+8 x^{3 n}}{4 x^{3 n}}$$

Will help you prepare for the material covered in the next section. In each exercise, find the indicated products. Then, if possible, state a fast method for finding these products. (You may already be familiar with some of these methods from a high school algebra course.) a. \((x+3)(x+4)\) b. \((x+5)(x+20)\)

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. There are many exponential expressions that are equal to \(36 x^{12},\) such as \(\left(6 x^{6}\right)^{2},\left(6 x^{3}\right)\left(6 x^{9}\right), 36\left(x^{3}\right)^{9},\) and \(6^{2}\left(x^{2}\right)^{6}\)

In Exercises \(79-82,\) simplify each expression. $$\frac{2 x^{3}(4 x+2)-3 x^{2}(2 x-4)}{2 x^{2}}$$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

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.