/*! 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 29 Assume that all variables repres... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 29

Assume that all variables represent nonzero real numbers. $$ 3^{0}+(-3)^{0} $$

Short Answer

Expert verified
2

Step by step solution

01

Understand Zero Exponent Rule

The zero exponent rule states that any nonzero number raised to the power of 0 is 1. That is, for any nonzero number a, we have: a^0 = 1
02

Apply Zero Exponent Rule to Each Term

Using the zero exponent rule, we can evaluate each term separately:For the first term: 3^0 = 1For the second term: (-3)^0 = 1
03

Sum the Results

Now, add the results from both terms:1 + 1 = 2

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.

exponents
Exponents are a way to represent repeated multiplication of the same number by itself. In expressions like \( a^n \), the number 'a' is called the base, and 'n' is the exponent. It means 'a' is multiplied by itself 'n' times. For example, in \( 2^3 \), the base is 2, and the exponent is 3, so it equals 2 脳 2 脳 2 which is 8.
Exponents follow several rules such as:
  • Product of Powers Rule: \( a^m \cdot a^n = a^{m+n} \)
  • Power of a Power Rule: \( (a^m)^n = a^{m \times n} \)
  • Zero Exponent Rule: \( a^0 = 1 \) for any nonzero 'a'
Understanding and applying these rules correctly helps simplify and solve complex expressions involving exponents.
real numbers
Real numbers include all the numbers you can think of, except for imaginary numbers. They encompass:
  • Natural Numbers: Counting numbers like 1, 2, 3, ...
  • Whole Numbers: Natural numbers including 0
  • Integers: Whole numbers and their negative counterparts like -2, -1, 0, 1, 2, ...
  • Rational Numbers: Numbers that can be expressed as a fraction \( \frac{p}{q} \) where p and q are integers, and q 鈮� 0
  • Irrational Numbers: Numbers that cannot be expressed as a simple fraction, like \( \pi \) and \( \sqrt{2} \)
Understanding real numbers is crucial because they form the basis of most algebraic expressions and equations.
In the problem \( 3^0 + (-3)^0 \), 3 and -3 are real numbers, and the expression follows the rules of real numbers and exponents.
evaluating expressions
Evaluating expressions involves simplifying them to find their value. Let鈥檚 take the expression \( 3^0 + (-3)^0 \) and break it down step-by-step:
1. Understand the Zero Exponent Rule: Any nonzero number raised to the power of 0 is 1. This rule simplifies our task.
2. Apply the Rule: Evaluate each part of the expression using the zero exponent rule:
  • \( 3^0 = 1 \)
  • \( (-3)^0 = 1 \)
3. Add the Results: Finally, add the values we got from each part:
\( 1 + 1 = 2 \)
This process shows how understanding the rules and systematically applying them ensures you get the correct value when evaluating expressions.
Practice with different expressions to get more comfortable with these rules!

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 each number in standard notation. $$ 5.42 \times 10^{-4} $$

Find each product. $$ (3 r+2 s)\left(r^{3}+2 r^{2} s-r s^{2}+2 s^{3}\right) $$

Simplify each expression so that no negative exponents appear in the final result. Assume that all variables represent nonzero real numbers. $$ \left(\frac{3 k^{-2}}{k^{4}}\right)^{-1} \cdot \frac{2}{k} $$

Simplify each expression so that no negative exponents appear in the final result. Assume that all variables represent nonzero real numbers. $$ \frac{\left(3 r^{2}\right)^{2} r^{-5}}{r^{-2} r^{3}}\left(2 r^{-6}\right)^{2} $$

Simplify each expression so that no negative exponents appear in the final result. Assume that all variables represent nonzero real numbers. $$ \left(\frac{2 p}{q^{2}}\right)^{3}\left(\frac{3 p^{4}}{q^{-4}}\right)^{-1} $$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Applied 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.