Complete guide
Exponent calculator that solves base, exponent or result
Select the missing quantity, enter the other two and see the inverse check. The result also lists nearby integer powers for scale.
What an exponent means
For a positive whole-number exponent, bⁿ is repeated multiplication. Zero, negative and fractional exponents extend the operation through algebraic rules.
Three equations
The selected mode decides which inverse operation is valid in the real domain.
y=bˣx=ln(y)/ln(b)b=y^(1/x)Negative and zero exponents
A negative exponent takes a reciprocal. For nonzero b, b⁰=1. Zero raised to zero or a negative exponent is left undefined here.
Fractional exponents
An exponent 1/n represents an nth root when a real root exists. Negative bases with noninteger exponents can require complex numbers and are rejected.
Worked inverse example
Since 2 multiplied by itself eight times equals 256, solving x in 2ˣ=256 returns 8.
Precision and scale
Large powers can overflow ordinary floating-point numbers and close decimal exponents can round. The result and inverse check make that numerical limit visible.
Core exponent rules
| Rule | Identity |
|---|---|
| Product | bᵐbⁿ=bᵐ⁺ⁿ |
| Quotient | bᵐ/bⁿ=bᵐ⁻ⁿ |
| Power of power | (bᵐ)ⁿ=bᵐⁿ |
| Negative | b⁻ⁿ=1/bⁿ |
| Fractional | b^(1/n)=nth root of b |
Frequently asked questions
What is any nonzero number to power zero?
It equals 1.
What does a negative exponent mean?
It takes the reciprocal of the positive power.
Can the base be negative?
Yes when calculating a power with an integer exponent.
Why can a fractional power be rejected?
A negative base can require a complex result.
How is the exponent recovered?
Use ln(result)/ln(base) for a positive valid base other than one.
Which base is returned when solving?
The calculator returns the positive real base.
What to keep in mind
The tool stays in the real-number system. Negative bases require an integer exponent; solving a base returns the positive real root. Zero to a nonpositive power is undefined.
Results display up to 8 decimal places; exported numbers preserve calculation precision. This is a calculation summary, not an official certificate.