/*! 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 237 In the following exercises, simp... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 237

In the following exercises, simplify. $$\text{(a)}(10 p)^{0} \quad \text { (b) } 10 p^{0}$$

Short Answer

Expert verified
(10p)^0 = 1; 10p^0 = 10

Step by step solution

01

- Understand the Zero Exponent Rule

The zero exponent rule states that any non-zero number raised to the power of zero equals one. Mathematically, this can be written as: \[ a^0 = 1 \] where \(a\) is any non-zero number.
02

- Apply the Zero Exponent Rule to (10p)^0

According to the zero exponent rule, any expression raised to the power zero is 1. Therefore, \[ (10p)^0 = 1 \]
03

- Address Parentheses in the First Expression

It is important to note that the entire expression \((10p)\) is raised to the power zero. So, regardless of the values of 10 and \(p\), \[ (10p)^0 = 1 \]
04

- Simplify 10p^0

In the expression \(10p^0\), only \(p\) is raised to the power of zero. According to the zero exponent rule, \[ p^0 = 1 \] Therefore, the expression becomes: \[ 10 \times 1 = 10 \]

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.

zero exponent rule
The zero exponent rule is a fundamental concept in algebra. It states that any non-zero number raised to the power of zero equals one. This can be represented mathematically as: \[ a^0 = 1 \]where \(a\) is any non-zero number.
This rule helps simplify expressions in algebra, making calculations easier. For example, in the exercise given, \[ (10p)^0 \]is simplified to one by applying the zero exponent rule, resulting in:\[ (10p)^0 = 1 \]Similarly, in the expression \[ 10p^0 \]only the \(p\) is raised to the zero power. Thus, it simplifies to:\[10 \times 1 = 10\]Understanding and applying this rule correctly allows for easy simplification of complex mathematical expressions.
simplifying exponents
Simplifying exponents involves applying rules to make expressions easier to work with. The zero exponent rule is just one of many exponent rules. Others include the product of powers rule, quotient of powers rule, and power of a power rule.
Here's a quick primer on these rules:
  • Product of Powers: \(a^m \times a^n = a^{m+n}\)
  • Quotient of Powers: \(\frac{a^m}{a^n} = a^{m-n}\)
  • Power of a Power: \((a^m)^n = a^{m \times n}\)
Applying these rules helps break down expressions and simplify calculations. For example:\((2^3 \times 2^2) = 2^{3+2} = 2^5 = 32\)
For the exercise given:\[(10p)^0 = 1\]is a direct application of the zero exponent rule, making the expression simple and straightforward.
mathematical expressions
Mathematical expressions are combinations of numbers, variables, and operators that represent values and operations. Simplifying these expressions involves applying rules and properties of operations to make them easier to understand and use.
For instance, in the expression:\[ (10p)^0 \]we use the zero exponent rule to simplify it to:\[ 1 \]
Similarly, for the expression \[ 10p^0 \]simplifying the exponent first by applying the zero exponent rule gives us:\[ 10 \times 1 = 10 \]
Learning how to read and simplify mathematical expressions is fundamental in prealgebra, as it builds a strong foundation for tackling more advanced algebraic problems in the future.

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

Simplify. $$(14 t)^{0}$$

Simplify. $$\left(\frac{x}{2}\right)^{5}$$

Write each number in scientific notation. According to www.cleanair.com, U.S. businesses use about 21,000,000 tons of paper per year.

Simplify each expression. $$(n-8)\left(n^{2}-4 n+11\right)$$

Simplify each expression. $$\frac{x^{4}}{x^{-5}}$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Applied Mathematics

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.