Exponent Rules
Learn the product, quotient, power, zero, negative, and fractional exponent rules with examples and one complete simplification.
Exponent rules tell you when to add, subtract, or multiply powers and how to rewrite zero, negative, and fractional exponents.
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7 formulas, different jobs
Exponent rules tell you when to add, subtract, or multiply powers and how to rewrite zero, negative, and fractional exponents.
Product Rule
Use it when multiplying powers with the same base.
Quotient Rule
Use it when dividing powers with the same nonzero base.
Power of a Power
Use it when one power is raised to another power.
Power of a Product
Use it to distribute an exponent across multiplication.
Zero Exponent Rule
Use it whenever a nonzero base has exponent zero.
Negative Exponent Rule
Use it to rewrite a negative exponent with a positive exponent.
Fractional Exponent Rule
Use it to move between rational exponents and radicals.
Simplify one expression with three rules
Simplify (2x³y⁻²)² ÷ (4xy⁻¹) by applying the power, quotient, and negative-exponent rules in order.
- 1 · Power
- 2 · Divide
- 3 · Make positive
- 4 · Restriction
Common mistakes
- Adding exponents when the bases are different.
- Applying a power to only one factor inside parentheses.
- Treating a negative exponent as a negative value instead of a reciprocal.
See which formulas your problem uses
Enter a problem and get a step-by-step solution with the formulas and theorems identified.
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Exponent rules FAQ
Do I add exponents when adding terms?
No. You add exponents only when multiplying powers with the same base. Addition follows the ordinary rules for like terms.
Is zero to the zero power covered by the zero exponent rule?
No. The rule a⁰ = 1 assumes a is nonzero; 0⁰ needs separate context and is not handled by this rule.