When is the quotient of two monomials a monomial?
The quotient of two monomials is a monomial when the variables have the same exponent and the coefficients can be divided. To understand this concept better, let's break it down into steps:
Step 1: Review Monomials
A monomial is an algebraic expression that consists of a single term. It can be written in the form: coefficient * variable ^ exponent. For example, 2x^2 is a monomial because it has a coefficient of 2, a variable x with an exponent of 2. Another monomial could be 3y^3, where the coefficient is 3 and the variable y has an exponent of 3.
Step 2: Compute the Quotient
To find the quotient of two monomials, divide the coefficients and subtract the exponents of the variables. For example, if we have (4x^3) / (2x), we can divide the coefficients (4 ÷ 2 = 2) and subtract the exponents (3 - 1 = 2). Therefore, the quotient is 2x^2, which is a monomial.
Step 3: Check for Conditions
To determine if the quotient of two monomials is a monomial, you need to ensure that the variables have the same exponent and that the coefficients can be divided evenly. If the variables have different exponents or the coefficients cannot be divided, the quotient will not be a monomial. For example, (5x^2) / (3x^3) does not result in a monomial because the variable exponents are different (2 ≠ 3).
In summary, the quotient of two monomials is a monomial when the variables have the same exponent, and the coefficients can be divided. Remember to check these conditions to determine whether or not the quotient is a monomial.