Definition: A monomial is a polynomial with exactly one term: a number, a variable, or a product of a number and variables with whole-number exponents.
What is a monomial?
The prefix mono means one. Examples are 9, y, -3x2, and 0.5ab3. There is no addition or subtraction between pieces.
How do you work with monomials?
To multiply, multiply the coefficients and add exponents of matching variables. To divide, divide the coefficients and subtract exponents. To raise to a power, raise the coefficient and multiply each exponent.
Example. Multiply (-4x3y)(6x2y5). Coefficients: -4 times 6 is -24. For x: 3 + 2 = 5. For y: 1 + 5 = 6. The product is -24x5y6. Now raise (2m4)3: 2 cubed is 8, and 4 times 3 is 12, giving 8m12.
Which errors are common?
Learners add exponents when raising a power to a power, or forget to cube the coefficient. A variable alone, like y, has exponent 1. Expressions such as 3x + 2 are not monomials, and neither is 5 / x.