Monomial Algebra Calculator
Perform multiplication, division, and power operations on algebraic monomials. Features visual grouping of coefficients and exponents.
Try these examples:
About
Beginners in algebra often struggle to distinguish between operations performed on coefficients and those performed on exponents. This tool isolates monomials - single algebraic terms like 4x2y - to demonstrate the mechanics of variable manipulation. It handles multiplication, division, and exponentiation.
Accuracy in these operations is foundational for factoring polynomials and solving differential equations later in a curriculum. The output explicitly separates the numerical calculation from the variable rules, using color coding to trace the logic of exponent laws.
Formulas
When multiplying two monomials M1 and M2:
Where c represents the coefficients and x,y are variables.
Reference Data
| Rule Name | Algebraic Definition | Example |
|---|---|---|
| Product of Powers | xa ⋅ xb = xa+b | x2 ⋅ x3 = x5 |
| Quotient of Powers | xaxb = xa−b | y5 ÷ y2 = y3 |
| Power of a Power | (xa)b = xa⋅b | (z3)4 = z12 |
| Power of a Product | (xy)a = xaya | (2x)2 = 4x2 |
| Zero Exponent | x0 = 1 if x ≠ 0 | 50 = 1 |
| Negative Exponent | x−a = 1xa | x−2 = 1/x2 |