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Chapter 1: Problem 32

Evaluate each of the following for x = -2. $$ (-x)^{0} $$

Short Answer

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Step by step solution

01

- Substitute the value of x

Replace the variable \( x \) with the given value \( -2 \). The expression becomes \( (-(-2))^{0} \).
02

- Simplify inside the parentheses

Evaluate the inner expression inside the parentheses. Since \( -(-2) = 2 \), the expression now is \( 2^{0} \).
03

- Apply the zero exponent rule

According to the zero exponent rule, any number raised to the power of zero is 1: \( 2^{0} = 1 \).

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Key Concepts

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

Substitute Variable
When solving math problems that include variables, one essential step is to substitute the given value for the variable. In this case, we are given a value for \( x \), which is -2.

Here's how we do it:
  • Identify the variable in the expression.
  • Replace the variable with the given number.

This process helps in simplifying the problem. For this exercise, substituting \( x \) with -2 in the expression \( (-x)^{0} \) changes it to \( (-(-2))^{0} \). After substitution, we can move on to the next steps.
Simplify Expression
Simplifying an expression means making it as simple as possible. After substituting the value for the variable, we need to evaluate the inner expression inside the parentheses.

In our problem, the substitution gave us \( (-(-2))^{0} \). Now we need to simplify inside the parentheses:
  • Evaluate the inner part, which is \( -(-2) \).
  • Since a negative of a negative number is a positive, \( -(-2) \) becomes 2.

So, the expression is now simplified to \( 2^{0} \). This makes it easier to apply any exponent rules in subsequent steps.
Exponents
Exponents express how many times a number, called the base, is multiplied by itself. In our simplified expression, which is now \( 2^{0} \), the exponent is 0.

Here鈥檚 the key point about the zero exponent: any non-zero number raised to the power of zero is always 1.

This is known as the zero exponent rule. Applying this rule here means:
  • The expression \( 2^{0} \) equals 1.

So, the final value of the expression is 1. Remembering this fundamental rule about exponents can make solving such problems straightforward.

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Most popular questions from this chapter

Find an equivalent expression by factoring. $$ 6 y-9 x-3 w $$

Classify each statement as either true or false. The following sets are used: \(\mathrm{N}=\) the set of natural numbers; \(W=\) the set of whole numbers; \(\mathbb{Z}=\) the set of integers; \(\mathbb{C}=\) the set of rational numbers; \(\mathrm{H}=\) the set of irrational numbers; \(\mathrm{R}=\) the set of real numbers. $$ \mathrm{H} \subseteq R $$

Write an equivalent expression using the distributive law. $$ -2(3 c+5 d) $$

Use set-builder notation to write each set. The set of all multiples of 5 between 7 and 79

Calculate using the rules for order of operations. If an expression is undefined, state this. $$ 32-(-5)^{2}+15 \div(-3) \cdot 2 $$
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