Exponent Calculator
Calculate powers, roots, and exponential expressions with step-by-step solutions.
| n | base^n | Scientific |
|---|---|---|
| Enter a base to see the table | ||
Calculate any power b^n, convert numbers into and out of scientific notation, or find nth roots, with the expanded step-by-step working shown for each.
How Exponent Calculator Works
Standard mode raises a base b to an exponent n directly. Integer exponents work exactly as you'd expect (repeated multiplication), but the calculator also handles fractional exponents (entered as a decimal, or typed as a fraction like 1/3 which is automatically converted) and negative exponents, which flip the result into a reciprocal: b^(−n) = 1/(b^n).
Scientific mode multiplies a coefficient a by 10 raised to a chosen power n, letting you convert between a compact scientific-notation form (like 3.5 × 10⁶) and its full standard decimal equivalent in either direction.
Root mode computes the nth root of a number x as x^(1/n) — a square root is simply the 2nd root, a cube root the 3rd — and then verifies the answer by raising the computed root back to the nth power to confirm it returns to the original value.
See It In Action
Who Uses Exponent Calculator and Why
- Computing a large power like 2^10 for a computer science or algebra problem.
- Converting a measurement between standard decimal form and scientific notation for a physics or chemistry class.
- Finding an nth root of a number and verifying it by raising the result back to the same power.
- Working with a negative exponent to represent a reciprocal or decay factor in a formula.
Mistakes to Avoid
- Assuming a negative exponent produces a negative result — it actually means 'take the reciprocal,' so 2^(−3) = 1/8, a positive number.
- Typing a fractional exponent as a rounded decimal (like 0.33 instead of the fraction 1/3), which loses precision compared to using the dedicated fraction input.
- Expecting the log(result) field to show a value when the base/exponent combination produces a zero or negative result — logarithms are only defined for positive numbers.
Tips for Best Results
- Use the 'enter as fraction' field for exact roots like 1/3 or 1/4 rather than typing an approximate decimal exponent.
- Remember a negative exponent flips the result into a reciprocal — it never changes the sign of the base.
Fixing Common Problems
The log(result) field shows undefined. — This happens when your base/exponent combination produces a zero or negative result — for example, a negative base raised to an odd power. Logarithms have no defined value for non-positive numbers.
Terms Explained
Reciprocal: The result of 1 divided by a number — what a negative exponent produces from its positive-exponent counterpart.
Scientific notation: A way of writing very large or small numbers as a coefficient between 1 and 10 multiplied by 10 raised to a power.