Exponent Calculator
Powers and whole degree roots with inverse and rebuild checks shown.
What it does
Exponents count repeated multiplication: ten copies of 2 make 1024, three copies of 5 make 125. Roots run the film backwards, asking which base rebuilds the value in n copies.
The tool above takes a base with an exponent or a root degree. It returns the result with the reciprocal and a rebuild check beside them.
The default of 2^10 gives 1024 with reciprocal 0.000977, and raising the magnitude back to 1/10 rebuilds 2. Flipping to root mode, 27 with degree 3 gives 3, which cubes back to 27.
The rules follow standard college algebra exponent references with open textbook treatments matching each identity. Both agree that negative exponents reciprocate and zero exponents return 1.
How to use
- Pick power for base^exponent or root for the nth root.
- Enter the base number.
- Enter the exponent, or the whole root degree 2 to 100.
- Read the result first.
- Use the check line to verify the round trip.
Formula
- base
- Number multiplied or under the radical.
- n
- Exponent, or whole root degree.
- 1/n
- Fractional power defining the nth root.
Even roots of negatives have no real answer and are rejected plainly. Odd roots of negatives stay real: the cube root of -8 is -2. Huge powers that overflow are rejected instead of printing infinity.
Worked example
Example: 2^10
Defaults: power mode, base 2, exponent 10.
- Multiply: 2 x 2 ten times = 1024.
- Reciprocal: 1 / 1024 = 0.000977.
- Check: 1024^(1/10) = 2, the base magnitude.
- Negative twin: 2^-10 would read 0.000977 directly.
- Tool shows 1024, 0.000977, 2 rebuilds the base magnitude.
Reference table
| Input | Result | Reciprocal |
|---|---|---|
| 2^10 | 1024 | 0.000977 |
| 5^3 | 125 | 0.008 |
| 10^6 | 1000000 | 0.000001 |
| 3rd root of 27 | 3 | 0.333333 |
Limits
- Real answers only; complex roots sit outside.
- Exponents cap at 1000 in magnitude to dodge overflow.
- Root degrees cap at whole numbers 2 to 100.
- Float display rounds at 6 places past trailed exactness.
Common mistakes
- Multiplying base by exponent instead of repeated multiplying.
- Adding exponents across different bases.
- Expecting a real answer for even roots of negatives.
- Reading 2^3^2 left to right instead of top down.
- Confusing 0^0 forms with the plain nonzero^0 = 1 rule.
Try it yourself
Quick checks. Answers sit tucked under each question.
4th root of 16?
2, since 2^4 = 16 (reciprocal 0.5).
Square root of -4?
Rejected: negatives need an odd degree for a real root.
2 to the -3?
0.125 with reciprocal 8: negative exponents flip.
Questions
What is 2^10?
1024: ten copies of 2 multiplied.
How do negative exponents work?
They reciprocate: 2^-3 is 1/8 = 0.125.
What is any number to the 0?
1 for nonzero bases. The tool labels that case plainly.
Root or fractional power?
Same thing: the nth root is the 1/n power. Cube root of 27 is 27^(1/3) = 3.
Why no even root of negatives?
No real number squares to a negative. Odd degrees still work.
Power rules for same bases?
Multiply by adding exponents, divide by subtracting them.