Simplify Exponents Calculator
Combine exponents for products, quotients, and powers with the same base. The calculator shows the rule, rewrites negative powers, and can verify the result using a numeric base.
Written and checked by TheToolNet Editorial Team · Last reviewed: September 19, 2026
Simplify an exponent expression
Exponent rules for the same base
| Operation | Rule | Example |
|---|---|---|
| Multiply | xᵐxⁿ = xᵐ⁺ⁿ | x³x⁴ = x⁷ |
| Divide | xᵐ/xⁿ = xᵐ⁻ⁿ | x⁷/x² = x⁵ |
| Power of a power | (xᵐ)ⁿ = xᵐⁿ | (x³)² = x⁶ |
| Negative power | x⁻ⁿ = 1/xⁿ | x⁻³ = 1/x³ |
These combination rules require the same base. Do not combine x² and y³ merely because both have exponents. Division and negative exponents also require a nonzero base.
Fractions and negative exponents
A negative exponent indicates a reciprocal, not a negative value. For example, 2⁻³ = 1/2³ = 1/8. A fractional exponent describes a root: x1/2 = √x and xm/n is the nth root of xm, subject to real-number domain restrictions.
Frequently asked questions
What is any nonzero number to the zero power?
It is 1. The expression 0⁰ is context-dependent and is not treated as an ordinary exponent-rule result here.
Can I simplify exponents with variables?
Yes. Enter a variable symbol and the two exponents; the optional numeric base is only for verification.
How do I enter exponents on a calculator?
See the calculator exponent-key guide.