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Chapter 5: Problem 20

Multiply. $$ \left(-5 n^{3}\right)(-1) $$

Short Answer

Expert verified
The product is \(5 n^{3}\).

Step by step solution

01

Interpret the Expression

The expression \( \left(-5 n^{3}\right)(-1)\) consists of two terms: \(-5 n^{3}\) and \(-1\). The multiplication involves combining these terms properly.
02

Multiply the Coefficients

First, focus on the coefficients of the terms. Multiply -5 by -1. Since \-5 \times -1\ gives a positive result \((5)\). Hence, the coefficient part of the product is 5.
03

Consider the Variables

Next, look at the variable part. There is no other variable term besides \(n^{3}\). Thus, the variable part remains \(n^{3}\).
04

Combine the Results

Combine the coefficient and the variable part. The resulting expression is \(5 n^{3}\).

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Key Concepts

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

Coefficients
In algebra, coefficients are the numbers that multiply the variables. They are the numerical part of a term and dictate the term's magnitude. For instance, in \(-5 n^{3}\), \(-5\) is the coefficient. Coefficients can be positive or negative.
When multiplying terms:
  • Multiply the coefficients separately from the variables.
  • Ensure to follow basic multiplication rules. For example, \[ -5 \times -1 = 5 \]. Multiplying two negative numbers results in a positive number.
By isolating the coefficient part first, you can simplify the expression easily. It makes handling complex equations more manageable.
Variables
Variables are symbols used to represent numbers whose values are not yet known. In most algebraic expressions, letters like \( n\) serve as variables. They can have exponents that indicate the power to which the variable is raised, such as \( n^{3}\).
Here's how to handle variables:
  • Look at each term and note the variables and their exponents.
  • When there are no other variables to multiply, simply carry the variable part over to the final product. For instance, \( n^{3}\) remains \( n^{3}\) when multiplied by -1.
Understanding variables is essential to mastering algebra. Treat them carefully during multiplication.
Negative Numbers
Negative numbers are less than zero and are indicated with a minus sign \( - \). They follow specific rules during multiplication:
  • Multiplying two negative numbers yields a positive result. For example, \[ -5 \times -1 = 5 \].
  • When a negative number is multiplied by a positive, the result is negative. This is not the case here.
Recognizing these rules helps to avoid mistakes. In our example, multiplying the coefficients \( -5 \) and \( -1 \) results in a positive 5. Always pay attention to the signs.

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Most popular questions from this chapter

Simplify. Assume that no denominator is zero and that \(0^{0}\) is not considered. $$ \left(\frac{x^{5}}{y^{2}}\right)^{7} $$

Use the fact that \(10^{3} \approx 2^{10}\) to estimate each of the following powers of \(2 .\) Then compute the power of 2 with a calculator and find the difference between the exact value and the approximation. $$ 2^{22} $$

Use the fact that \(10^{3} \approx 2^{10}\) to estimate each of the following powers of \(2 .\) Then compute the power of 2 with a calculator and find the difference between the exact value and the approximation. $$ 2^{31} $$

Simplify. Write \(8^{-3} \cdot 32 \div 16^{2}\) as a power of 2

If \(f(x)=c,\) where \(c\) is some positive constant, describe how the graphs of \(y=g(x)\) and \(y=(f+g)(x)\) will differ.
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