Multiply, divide, or raise monomials using exponent rules
Result
Simplified Monomial
Step-by-Step Derivation
Monomial Operation Formulas
(axᵐ)(bxⁿ)=abxᵐ⁺ⁿ, (axᵐ)/(bxⁿ)=(a/b)xᵐ⁻ⁿ
Monomial rules handle coefficients and exponents separately. Coefficients multiply or divide normally, while matching variable powers add, subtract, or multiply exponents depending on the operation.
⚠Note: This tool assumes all monomials use the same variable x. Division by a zero coefficient is not allowed.
How Monomial Rules Work
Simplify the number part and the variable-power part separately, then put them back into one monomial.
Coefficient Rule
Coefficients are multiplied, divided, or exponentiated normally.
Product Rule
x^m × x^n = x^(m+n).
Quotient Rule
x^m / x^n = x^(m-n), when x is not zero.
Power Rule
(x^m)^n = x^(mn).
💡 Example: (3x²)(-2x³) = -6x⁵ because 3×(-2)=-6 and 2+3=5.
Applications of Monomial Operations
Exponent RulesExpression SimplificationPolynomial TermsAlgebra Practice
Frequently Asked Questions
What is a monomial calculator?▼
A monomial calculator performs operations on single-term expressions such as 3x² or -5x⁴.
How do you multiply monomials?▼
Multiply the coefficients and add exponents with the same variable.
How do you divide monomials?▼
Divide the coefficients and subtract the exponent in the denominator from the exponent in the numerator.
How do monomial powers work?▼
Raise the coefficient to the power and multiply the variable exponent by that power.
Can a monomial have a negative exponent?▼
Yes. A negative exponent means the variable belongs in the denominator when written with positive exponents.
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