Question
How do I find the degree of monomials
Answers
GPT-4o mini
The degree of a monomial is the sum of the exponents of its variables. Here are the steps to find the degree:
1. **Identify the monomial**: A monomial is an algebraic expression that consists of a single term. It can be a number, a variable, or a product of numbers and variables. For example, \(3x^2y^3\) and \(7\) are both monomials.
2. **Examine the exponents**: Look at each variable in the monomial and note its exponent. If a variable does not have an explicit exponent, it is understood to be 1. For instance, in \(x^2\), the exponent is 2, and in \(x\), the exponent is 1.
3. **Sum the exponents**: Add together the exponents of all the variables. For example, in the monomial \(3x^2y^3\):
- The exponent of \(x\) is 2.
- The exponent of \(y\) is 3.
- The degree is \(2 + 3 = 5\).
4. **Consider the constant**: If the monomial is just a constant (like \(7\)), it has no variable terms, and its degree is 0.
### Examples:
1. **Monomial**: \(5x^4\)
- Degree: \(4\) (only the \(x\) term counts)
2. **Monomial**: \(2x^3y^2z^1\)
- Degree: \(3 + 2 + 1 = 6\)
3. **Monomial**: \(4\)
- Degree: \(0\) (it's a constant)
That's how you find the degree of monomials!
1. **Identify the monomial**: A monomial is an algebraic expression that consists of a single term. It can be a number, a variable, or a product of numbers and variables. For example, \(3x^2y^3\) and \(7\) are both monomials.
2. **Examine the exponents**: Look at each variable in the monomial and note its exponent. If a variable does not have an explicit exponent, it is understood to be 1. For instance, in \(x^2\), the exponent is 2, and in \(x\), the exponent is 1.
3. **Sum the exponents**: Add together the exponents of all the variables. For example, in the monomial \(3x^2y^3\):
- The exponent of \(x\) is 2.
- The exponent of \(y\) is 3.
- The degree is \(2 + 3 = 5\).
4. **Consider the constant**: If the monomial is just a constant (like \(7\)), it has no variable terms, and its degree is 0.
### Examples:
1. **Monomial**: \(5x^4\)
- Degree: \(4\) (only the \(x\) term counts)
2. **Monomial**: \(2x^3y^2z^1\)
- Degree: \(3 + 2 + 1 = 6\)
3. **Monomial**: \(4\)
- Degree: \(0\) (it's a constant)
That's how you find the degree of monomials!