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Chapter 5: Problem 14

Identify the base and the exponent in each expression. $$ -6 n^{0} $$

Short Answer

Expert verified
Base: n, Exponent: 0.

Step by step solution

01

Identify the Variables

Look at the given expression: -6 n^{0}. Notice that the variable here is n.
02

Identify the Base

In the expression -6 n^{0}, the base is the variable raised to the power. Here, the base is n.
03

Identify the Exponent

The exponent is the power to which the base is raised. In -6 n^{0}, the exponent is 0.
04

Understand the Coefficient

Recognize that -6 is the coefficient, which multiplies the term n^{0}. While this exercise focuses on the base and exponent, identifying the coefficient helps in understanding the whole expression.

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Key Concepts

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

Base
In mathematics, the term 'base' refers to the number or variable that is being multiplied by itself a certain number of times. In the expression given in the exercise, -6 n^{0}, the base is the variable n. This is because n is the number that is raised to a power.The base tells us what number we will be repeatedly multiplying.Think of the base as the starting point of the exponentiation process. The higher the base, the larger the result when raised to an exponent. For example, in the expression 2^{3}, 2 is the base.
Exponent
The exponent is a small number written above and to the right of the base in an expression. It tells us how many times the base is multiplied by itself. In the expression,-6 n^{0}, the exponent is 0. When the exponent is 0, it means we are multiplying the base, which is n, zero times. A key point to remember is that any non-zero number or variable raised to the power of 0 is 1. This is why n^{0} equals 1 regardless of what n is. Knowing the value of the exponent helps us understand the value of the entire term.
Coefficient
The coefficient is the number that is multiplied by the variable in an algebraic expression. In the expression, -6 n^{0}, the coefficient is -6.The coefficient affects the magnitude of the entire term. It's important to not confuse the coefficient with the base or the exponent. It simply acts as a multiplier.For example, in the term 4x, 4 is the coefficient meaning we have 4 units of x. Coefficients can be positive or negative and greatly impact the final value of the expression.
Variables
Variables are symbols used to represent unknown values or quantities in mathematical expressions. In the exercise's expression, -6 n^{0}, the variable is n. Variables can take on different values depending on the context of the problem. They are essential for creating expressions, equations, and functions. In algebra, we use variables to generalize rules and solve for unknowns. In the expression 3y + 5, y is the variable which could be any number depending on what the equation or context asks us to find.

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Most popular questions from this chapter

Reinforcement In each of Exercises \(1-6\) match the product with the correct result from the column on the right. Choices may be used more than once. $$ 3 x^{2} \cdot 2 x^{4} $$ a) \(6 x^{8}\) b) \(8 x^{6}\) c) \(6 x^{6}\) d) \(8 x^{8}\)

Review simplifying expressions using the rules for order of operations (Section \(1.8)\) $$ (9-3)(9+3)+3^{2}-9^{2} $$

Find the slope of the line containing the points \((3,2)\) and \((-7,5) .[3.5]\)

Find a polynomial for the shaded area of each figure. A \(12-\mathrm{m}\) by \(12-\mathrm{m}\) mat includes a circle of diameter \(d\) meters for wrestling. Find a polynomial for the area of the mat outside the wrestling circle.

For each pair of functions fand \(g\), determine the domain of the sum, the difference, and the product of the two functions. $$ \begin{aligned} &f(x)=5 x-1\\\ &g(x)=2 x^{2} \end{aligned} $$
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