/*! 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 \(-(-6)^{0}\)... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 17

\(-(-6)^{0}\)

Short Answer

Expert verified
-1

Step by step solution

01

Understand the Exercise

The exercise requires simplifying the expression \(-(-6)^0\). It involves handling the exponent and the negative signs.
02

Simplify the exponent

When a number is raised to the power of zero, it equals 1, i.e., \((-6)^0 = 1\).
03

Apply the negative sign outside

Now, apply the outer negative sign to the result of the exponent from the previous step. Thus, \(-1 * 1 = -1\).

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
In mathematics, exponents are used to express repeated multiplication of a number by itself. For example, in the expression \(3^4\), the number 3 is the base, and 4 is the exponent. This means you multiply 3 by itself 4 times:

3 * 3 * 3 * 3 = 81.

An important rule about exponents is that any number (except 0) raised to the power of zero equals 1. So, \br> 6^0 = 1.
With this concept, the original exercise simplifies (-6)^0 to 1. It's helpful to remember these basic exponent rules when working through exponentiation problems.
Properties of Exponents
Understanding the key properties of exponents can simplify various mathematical problems. Here are some essential properties:

  • Product of Powers: When multiplying two exponents with the same base, you add the exponents:
    x^a * x^b = x^(a+b).
  • Power of a Power: When raising an exponent to another power, you multiply the exponents:
    (x^a)^b = x^(a*b).
  • Power of a Product: When raising a product to an exponent, you raise each factor to the exponent:
    (xy)^a = x^a * y^a.
  • Quotient of Powers: When dividing two exponents with the same base, you subtract the exponents:
    x^a / x^b = x^(a-b).
In the given exercise, the simplest property we use is that any number raised to the power of zero equals 1: (-6)^0 = 1.
Negative Numbers
Negative numbers are numbers less than zero. They are critical to understand in various mathematical contexts, including exponentiation. In our exercise, -(-6)^0, both a negative number and exponentiation are involved.

To dive deeper:

  • Negative Sign Outside: The expression -(-6)^0 has an outer negative sign. After simplifying the exponent part to 1, the outer negative sign changes the result to -1.
  • Negative Base: Interestingly, if the negative sign were inside the exponent, such as (-6)^0, it would still equal 1 because any non-zero number to the power of zero is 1.
Mastering the manipulation of negative numbers and understanding their interactions with exponents simplifies the solution to many problems.

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

Use scientific notation to calculate the result in each expression. Write answers in scientific notation. 75\. \(\frac{0.00000072(0.00023)}{0.000000018}\)

\(\frac{\left(2 y^{-1} z^{2}\right)^{2}\left(3 y^{-2} z^{-3}\right)^{3}}{\left(y^{3} z^{2}\right)^{-1}}\)

\begin{aligned} &\text { Find the difference of the sum of } 5 x^{2}+2 x-3 \text { and } x^{2}-8 x+2 \text { and the sum of } 7 x^{2}-3 x+6\\\ &\text { and }-x^{2}+4 x-6 \end{aligned}

The special product \((x+y)(x-y)=x^{2}-y^{2}\) can be used to perform some multiplications. Example: $$\begin{array}{l|l}51 \times 49 & 102 \times 98 \\\=(50+1)(50-1) & =(100+2)(100-2) \\\=50^{2}-1^{2} & =100^{2}-2^{2} \\\=2500-1 & =10,000-4 \\\=2499 & =9996\end{array}$$ Use this method to calculate each product mentally. $$ 101 \times 99 $$

Perform each indicated operation. \(\left[\left(9 b^{3}-4 b^{2}+3 b+2\right)-\left(-2 b^{3}-3 b^{2}+b\right)\right]-\left(8 b^{3}+6 b+4\right)\)
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

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.