/*! 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 11 Decide whether each expression i... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 11

Decide whether each expression is equal to \(0,1,\) or \(-1 .\) $$ \frac{0^{10}}{12^{0}} $$

Short Answer

Expert verified
The expression equals 0.

Step by step solution

01

Evaluate the numerator

The numerator of the expression is \(0^{10}\). Any number raised to any power is 0. Thus, \(0^{10} = 0\).
02

Evaluate the denominator

The denominator of the expression is \(12^{0}\). Any non-zero number raised to the power of 0 is 1. Thus, \(12^{0} = 1\).
03

Simplify the expression

Now, place the values from steps 1 and 2 into the original fraction: \(\frac{0}{1}\). This simplifies to 0.

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.

Exponent Rules
Understanding exponent rules is crucial in algebra. Exponents represent repeated multiplication. For example, in the term \(a^b\), \(a\) is the base, and \(b\) is the exponent. Here are some key rules:
  • Zero Exponent Rule: Any non-zero number raised to the power of 0 is 1. In our example, \(12^0 = 1\).
  • Power of Zero Rule: 0 raised to any positive number is always 0. For instance, \(0^{10} = 0\).
  • Product of Powers Rule: When multiplying like bases, you add the exponents (e.g., \(a^m * a^n = a^{m+n}\)).
  • Quotient of Powers Rule: When dividing like bases, you subtract the exponents (e.g., \(\frac{a^m}{a^n} = a^{m-n}\)).
Using these rules allows us to evaluate any expression involving exponents. Applying them step-by-step often makes complex problems simple.
Numerator and Denominator
In a fraction, the numerator is the top number, and the denominator is the bottom number. They represent parts of a whole:
  • Numerator: The number above the line in a fraction. It tells how many parts you have.
  • Denominator: The number below the line. It tells into how many parts the whole is divided.
In our case, the fraction is \(\frac{0^{10}}{12^0}\):
  • Numerator: Here, it's \(0^{10}\), which equals 0.
  • Denominator: Here, it's \(12^0\), which equals 1.
Understanding these explains how to properly place values into fractions and simplify them effectively.
Simplifying Fractions
Simplifying fractions means rewriting them in their simplest form. To do this, divide the numerator and the denominator by their greatest common factor (GCF). Here鈥檚 how to simplify:
  • Evaluate the numerator: If the numerator is 0 (like in \(\frac{0^{10}}{12^0}\)), the whole fraction is 0.
  • Evaluate the denominator: Ensure it's not zero because division by zero is undefined.
  • Divide both parts by their GCF: Here, the numerator is 0, and the denominator is 1. So, \(\frac{0}{1} = 0\).
This method ensures fractions are as simple as possible, making them easier to understand and use in calculations.

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 by writing each expression wth positive exponents. Assume that all variables represent nonzero real numbers. $$ \frac{\left(4 a^{2} b^{3}\right)^{-2}\left(2 a b^{-1}\right)^{3}}{\left(a^{3} b\right)^{-4}} $$

Each statement comes from Astronomy! A Brief Edition by James B. Kaler (Addison-Wesley). If the number in boldface italics is in scientific notation, write it without exponents. If the number is written without exponents, write it in scientific notation. (IMAGE CANNOT COPY). The solar luminosity requires that \(2 \times 10^{9} \mathrm{kg}\) of mass be converted into energy every second. \((\text { page } 327)\).

Find each product. $$ (2 m+5)(2 m-5) $$

Match each number written in scientific notation I with the correct choice from Column II. Not all choices in Column II will be used. (I) (a) \(1 \times 10^{9}\) (b) \(1 \times 10^{6}\) (c) \(1 \times 10^{8}\) (d) \(1 \times 10^{10}\) (II) A. 1 billion B. 100 million C. 1 million D. 10 billion E. 100 billion

Find each product. $$ (3 m+1)^{3} $$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

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.