About

Algebraic manipulation often requires combining terms with exponents. This calculator handles the multiplication of two exponential terms, applying the Product of Powers Rule when bases match (x^a ⋅ x^b = x^a+b) and multiplying coefficients separately. It is designed to handle both numeric inputs and symbolic variables, making it useful for verifying homework answers or simplifying polynomial expressions.

Understanding how exponents aggregate is critical in fields ranging from computer science (complexity analysis) to physics (scientific notation). This tool ensures that rules regarding negative exponents and zero exponents are applied correctly.

Formulas

When multiplying two terms with the same base, add their exponents:

baseⁿ ⋅ base^m = base^{n + m}

If coefficients are present, multiply them:

(Axⁿ) × (Bx^m) = (A × B)x^{n + m}

Reference Data

Rule Name	Formula	Example Input	Result
Product of Powers	x^a ⋅ x^b = x^a+b	x² ⋅ x³	x⁵
Different Bases	x^a ⋅ y^b	x² ⋅ y³	x²y³
Coefficients	cx^a ⋅ dx^b = cdx^a+b	2x² ⋅ 3x⁴	6x⁶
Negative Exp	x^-a ⋅ x^b	x^-2 ⋅ x⁵	x³
Zero Exp	x⁰ = 1	x⁰ ⋅ x⁴	x⁴
Numeric Base	2³ ⋅ 2²	2³ ⋅ 2²	2⁵ = 32
Fractional Exp	x^1/2 ⋅ x^1/2	x^0.5 ⋅ x^0.5	x¹
Complex	axⁿ ⋅ by^m	4x² ⋅ 2y³	8x²y³

Frequently Asked Questions

Yes. The tool recognizes any single letter as a base. If the bases are different (e.g., x and y), they are simply placed next to each other in the result.

The tool adds the negative value algebraically. For example, 5 + (-2) results in an exponent of 3.

Yes, decimal exponents are added together. However, symbolic fraction exponents (like 1/2) should be converted to decimals or managed manually.

Any non-zero number raised to the power of 0 is 1. The calculator simplifies this automatically.