Multiplying Exponents Calculator
Calculate products of exponential terms using the Product Rule. Handles coefficients, variable bases, and negative exponents with step-by-step expansion logic.
About
Computing the product of exponential terms requires strict adherence to the Product Rule of exponents. This mathematical principle states that when multiplying terms with the same base, the exponents add while the coefficients multiply. Errors in this operation frequently cascade through complex algebraic derivations, particularly in calculus and physics applications where variable bases represent physical quantities.
This tool automates the process for expressions in the form c1xa ⋅ c2xb. It distinguishes between the arithmetic operation performed on coefficients and the additive operation applied to exponents. The logic handles integer, negative, and zero exponents, providing a visual breakdown of the factorization to validate the result.
Formulas
The core calculation relies on the Product Rule for Exponents:
When coefficients A and B are present:
Reference Data
| Expression Type | Rule Applied | General Formula | Example |
|---|---|---|---|
| Same Base | Product Rule | xa ⋅ xb = xa + b | x2 ⋅ x3 = x5 |
| Coefficients | Associative Property | (cxa) ⋅ (dxb) = cdxa + b | 2y2 ⋅ 3y4 = 6y6 |
| Negative Powers | Inverse Rule | x-n ⋅ xn = x0 = 1 | z-2 ⋅ z5 = z3 |
| Different Bases | No Simplification | xa ⋅ yb | a2 ⋅ b3 (Unchanged) |