Index Laws Calculator
Use the index laws for expressions with the same symbol base x. Enter integer exponents only.
A QUICK WALKTHROUGH
How to use this tool
- Choose multiplication, division, or a power of a power.
- Enter the shared base symbol and integer exponents.
- Read the simplified expression and its zero or negative exponent condition.
Rules used
xᵃ × xᵇ = xᵃ⁺ᵇ, xᵃ ÷ xᵇ = xᵃ⁻ᵇ, and (xᵃ)ᵇ = xᵃᵇ. The base is one symbol and every exponent is an integer.
Zero and negative exponents
x⁰ = 1 only when x ≠ 0. A negative exponent means a reciprocal, so x⁻ⁿ = 1/xⁿ and requires x ≠ 0. Division also requires x ≠ 0.
Reference
Rule wording follows OpenStax, Algebra and Trigonometry, section 1.6 “Properties of Exponents”.
GOOD TO KNOW
Common questions
Does this simplify different bases?
No. Both factors must use the same symbol base x.
Can I enter fractional exponents?
No. This calculator accepts integers only.
Why does division say x ≠ 0?
The denominator xᵇ must not be zero, and a negative resulting exponent is a reciprocal.