A monomial is an expression that is formed only by a **algebraic term only**, for example:

- P (x) = 4x²
- j (x, y, z) = 5x
^{3}y^{4}z^{2} - q (x, y) = x³y²

The expression p (x, y) = x²y + xy, is not a monomial, since it has **plus** of an algebraic term.

**How to multiply and divide a monomial**

To effectively achieve the multiplication and division of monomials, we must first take into account the sign, then the coefficients and finally the powers.

**Example 1**: Multiply the following monomials (5x³y) × (- 3y^{4}z)

Remembering the property of the power n^{a} × n^{b} = n^{a + b}, we have:

(5x³y) × (- 3y^{4}z) = - 15x^{3}y^{5}z

**Example 2**: Perform the following division of monomials (8x^{3}y^{3}z^{4}t) ÷ (-2xy^{2}z^{2})

Remembering the properties of powers n^{a} × n^{b} = n^{a + b }y 1 / n^{a} = n^{-to}, we have:

(8x^{3}y^{3}z^{4}t) ÷ (-2xy^{2}z^{2}) = -4x^{2}and Z^{2}t

**Example 3**: Multiply the following monomials (3x²y) × (7xy).

Remembering the property of the power n^{a} × n^{b} = n^{a + b}, we have:

(3x²y) × (7xy) = 21x³y²

**Example 4**: Carry out the following division of monomials (6x²y³) ÷ (-2xy).

Remembering the properties of powers n^{a} × n^{b} = n^{a + b }y 1 / n^{a} = n^{-to}, we have:

(6x²y³) ÷ (-2xy) = -3xy²