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Chapter 3: Problem 72

Evaluate \(-p^{2}\) for \(p=-1\) $$ [1.6] $$

Short Answer

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Step by step solution

01

Substitute the value of p

Replace the variable \( p \) with \( -1 \) in the expression \( -p^{2} \). This gives us: \( -(-1)^{2} \).
02

Evaluate the exponent

Calculate \( (-1)^{2} \). When raising \(-1\) to the power of 2, you get: \( (-1) \times (-1) = 1\).
03

Apply the negative sign

Apply the negative sign to the result obtained in Step 2. This results in: \( -1 \).

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Key Concepts

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

substitution in algebra
Substitution in algebra is a fundamental technique used to simplify expressions and solve equations. It involves replacing a variable with a specific value. In our exercise, we substitute the variable \( p \) with \( -1 \). Let's break this down further:

This is what happens when we substitute:
  • The original expression is \( -p^{2} \).
  • We replace \( p \) with \( -1 \), so it becomes \( -(-1)^{2} \).
By carrying out substitution, we make it easier to evaluate the expression. Always remember to carefully substitute the variable with its given value to avoid mistakes.
evaluating exponents
Evaluating exponents involves calculating the result of raising a number to a power. In our exercise, we need to find \( (-1)^{2} \). Here鈥檚 a step-by-step breakdown:

Understanding exponents:
  • When you see \( a^{b} \), it means you multiply \( a \) by itself \( b \) times.
For our specific example:
  • (-1)^{2} means multiplying -1 by itself twice.
  • This calculation can be written as: \( (-1) \times (-1) \).
  • Since multiplying two negative numbers results in a positive number, \( (-1) \times (-1) = 1 \).
Understanding how to evaluate exponents is crucial for solving algebraic expressions correctly.
negative numbers
Dealing with negative numbers can sometimes be confusing, but it is essential to understand their properties. In the given exercise, negative numbers play a key role. Let鈥檚 break down what happens:

When we substitute \( p \) with \( -1 \) and evaluate \( (-1)^{2} \), we need to know that:
  • Multiplying two negative numbers results in a positive number \( (-1 \times -1 = 1) \).


Finally, we apply the negative sign from the original expression to our result:
  • We started with the expression \( -p^{2} \).
  • Since \( (-1)^{2} = 1 \), the expression becomes \( -1 \).
Understanding the behavior of negative numbers helps you avoid mistakes and correctly simplify algebraic expressions.

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Most popular questions from this chapter

A low-flow shower aerator restricts the flow and increases the force of a shower, creating a fine spray that saves water and energy without compromising shower comfort. A 1.5 -gallon-per-minute aerator can save up to \(\$ 175\) per year if a standard efficiency electric water heater is in use. A new Niagara shower head, containing a low-flow aerator, was recently bought for \(\$ 8.14 .\) Assuming savings of \(\$ 175\) per year, how long will it take to break even on the purchase?

In triangle \(A B C,\) the measure of angle \(B\) is twice the measure of angle \(A .\) The measure of angle \(C\) is \(80^{\circ}\) more than that of angle \(A .\) Find the angle measures.

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Use a graphing calculator to solve each system of linear equations for \(x\) and \(y .\) Round all coordinates to the nearest hundredth. $$ \begin{aligned} 5.22 x-8.21 y &=-10.21 \\ -12.67 x+10.34 y &=12.84 \end{aligned} $$
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