Question

define each of the following:
a. term

b. base

c. exponent

d. coefficient

Explanation:

a. In algebra, a term is a single mathematical expression that can be a number, a variable, or a product of numbers and variables. For example, in the expression \(3x + 5\), \(3x\) and \(5\) are terms.
b. In an exponential expression of the form \(a^n\), the base is the number \(a\) that is being raised to a power. For example, in \(2^3\), \(2\) is the base.
c. In an exponential expression \(a^n\), the exponent is the number \(n\) that indicates how many times the base \(a\) is multiplied by itself. In \(2^3\), \(3\) is the exponent (meaning \(2\times2\times2\)).
d. A coefficient is a numerical factor in a term. In the term \(4x\), \(4\) is the coefficient, and in the term \(-5y^2\), \(-5\) is the coefficient. If a term is just a variable like \(x\), the coefficient is implicitly \(1\).

Answer:

a. A term is a single mathematical expression (number, variable, or product of them) in an algebraic expression (e.g., \(3x\), \(5\) in \(3x + 5\)).
b. In \(a^n\), the base is \(a\) (the number being raised to a power, e.g., \(2\) in \(2^3\)).
c. In \(a^n\), the exponent is \(n\) (shows how many times the base is multiplied, e.g., \(3\) in \(2^3\)).
d. A coefficient is the numerical factor of a term (e.g., \(4\) in \(4x\), \( - 5\) in \(-5y^2\)).