Exponent calculator
Evaluate powers with negative and fractional exponents.
What this calculator covers
Use this calculator to evaluate powers without separating negative exponents, roots, and ordinary repeated multiplication into different tools.
The explanation keeps the reciprocal or fractional-exponent interpretation visible so the result is easier to audit than a raw power output alone.
Frequently asked questions
- How does a negative exponent work?
- A negative exponent flips the base into a reciprocal. For example, 2^−3 equals 1 divided by 2^3, which is 1/8. The calculator shows this reciprocal interpretation alongside the decimal result so the relationship is clear.
- What does a fractional exponent mean?
- A fractional exponent like 1/2 or 0.5 represents a root. Specifically, x^(1/n) is the nth root of x, so 9^0.5 equals the square root of 9, which is 3. Any fraction in the exponent position combines a root with a power in the same expression.
- Why does the calculator reject a negative base with a non-integer exponent?
- Raising a negative number to a fractional power, such as (−4)^0.5, would require taking a square root of a negative number, which has no real-number solution. The calculator only returns real-valued results, so it rejects combinations that would produce complex numbers.
- Why is 0^0 treated as undefined here?
- The value of 0^0 is mathematically indeterminate — different limiting approaches yield different answers — so the calculator declines to return a single result for that input. Most computational contexts that do assign it a value use 1 as a convention, but this calculator takes the conservative position of leaving it undefined.
Tool
Run the calculation
Result
RESULT · POWER
â„–151
Primary result
3
9^0.5 = 3.
- Expression
- 9^0.5
- Fractional-exponent interpretation
- 9^0.5 = 3
- Result
- 3
Step-by-step solution
- 1.Start from base 9 and exponent 0.5.
- 2.A fractional exponent represents a root-and-power relationship, which JavaScript evaluates directly on the real-number line.
- 3.Evaluate the power and round the displayed result to 12 decimal places as 3.
Walkthrough
Visual walkthrough
Exponents compress repeated multiplication, reciprocal powers, and root relationships into one expression.
01
Read the base and exponent
9^0.5
The base is the starting quantity and the exponent determines whether the operation is repeated multiplication, a reciprocal, or a root-style power.
02
Apply the exponent rule
9^0.5 = 3
Negative exponents flip to reciprocals, and fractional exponents move through real-valued roots when the base allows it.
03
Read the solved power
3
The displayed result is rounded to 12 decimal places for consistency with the rest of the math set.
3