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Chapter 4: Problem 16

\(-6^{0}\)

Short Answer

Expert verified
The value of -6^{0} is -1.

Step by step solution

01

Understand the Zero Exponent Rule

When any non-zero number is raised to the power of zero, the result is always 1. This is known as the zero exponent rule.
02

Identify the Base

In the expression (-6^{0}), the base is -6. However, the exponent of zero applies only to the number 6, not the negative sign.
03

Apply the Zero Exponent Rule

Using the zero exponent rule, compute 6^{0}. According to the rule, 6^{0} = 1.
04

Attach the Negative Sign

Since the exponent applied only to 6, the negative sign remains. Thus, -6^{0} = -1.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

powers and exponents
Powers and exponents are fundamental concepts in algebra and many areas of mathematics.

An exponent indicates how many times a number, called the base, is multiplied by itself. For instance, in the expression \(6^2\), 6 is the base, and 2 is the exponent, meaning 6 is multiplied by itself.

To simplify, \[6^2 = 6 \times 6 = 36 \].

Whenever you see an exponent, remember it tells you to multiply the base by itself a certain number of times. This rule changes slightly with the Zero Exponent Rule.
algebraic expressions
Algebraic expressions are combinations of numbers, variables, and mathematical operations. Variables are symbols that represent numbers and can change value.

For example, in the expression \(-6^0\), -6 ties with 0 as an exponent.
To interpret algebraic expressions correctly, it is essential to understand the order of operations and how exponents work.

Here, applying the Zero Exponent Rule tells us to raise only the base 6 to power zero. Understanding algebraic expressions helps in operating complex numbers and symbols, leading to correct outcomes.
negative numbers
Negative numbers are numbers less than zero. They have a minus sign before them and represent values below zero.

When working with negative numbers in algebra, it鈥檚 crucial to understand how different mathematical operations affect them.

In the exercise \( -6^0 \), the base 6 is positive, but it is paired with a negative sign outside the exponent.
Following the Zero Exponent Rule, since any non-zero number raised to zero is 1, we get \[6^0 = 1 \], but the negative sign remains.

So, combining these rules: -6^0 gives us -1.

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Most popular questions from this chapter

Find each product. $$ -8 r^{3}\left(5 r^{2}+2\right)\left(5 r^{2}-2\right) $$

$$ \begin{aligned} &y=-x^{2}+2\\\ &\begin{array}{c|c} \hline x & y \\ \hline-2 & \\ \hline-1 & \\ \hline 0 & \\ \hline 1 & \\ \hline 2 & \end{array} \end{aligned} $$

In \(2016,\) the U.S. government collected about \(\$ 5712\) per person in individual income taxes. If the population of the United States at that time was 323,000,000 , how much did the government collect in taxes for \(2016 ?\) (Data from www.usgovernmentrevenue.com)

Use scientific notation to calculate the result in each expression. Write answers in scientific notation. 78\. \(\frac{0.000015(42,000,000)}{0.000009(0.000005)}\)

Find each product. Recall that \(a^{2}=a \cdot a\) and \(a^{3}=a^{2} \cdot a\). $$ -4 r(3 r+2)(2 r-5) $$
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