Exponent Calculator

Inputs

Base

Exponent

Decimal places

Rounding mode

Output

Scientific notation

Result

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waiting…

Steps

Enter base and exponent, then Calculate.

Exponent Calculator – Powers, Roots, and Exponents Online

Use this free Exponent Calculator to raise any base to a power or root. Enter a base (decimal or scientific notation) and an exponent (integer, decimal, or fraction like 1/2). The tool handles negative and fractional exponents, precise rounding, and optional scientific notation. Copy results and see the steps.

How to use the Exponent Calculator

Enter Base — e.g., 9, 2.5, or 1.2e-3.
Enter Exponent — integer (3), negative (−2), decimal (0.5), or fraction (1/2, 3/4).
Set Decimal Places & Rounding Mode — Half Up, Half Even (banker’s), Half Away, Half Down, Truncate, Floor, or Ceil.
(Optional) Enable Scientific Notation for very large/small results.
Click Calculate to see the result and step-by-step breakdown.

What can it do?

Powers: $a^n$ with positive/negative integers.
Roots: enter a fraction exponent like 1/2 (square root), 1/3 (cube root), or p/q.
Negative & fractional exponents: $a^{-n} = 1/a^n$ , $ap/q=apqa^{p/q} = \sqrt[q]{a^p}$ .
Scientific notation & rounding: choose decimal places and rounding rules to match science, finance, or engineering needs.
Exact integer powers: computed with high-precision arithmetic to avoid floating-point glitches.

Examples

$9^{1/2} = 3$ (square root)
$27^{1/3} = 3$ (cube root)
$2.5^3 = 15.625$
$10^{-3} = 0.001$
$16^{-1/2} = 0.25$
$(1.2×10−3)2=1.44×10−6(1.2\times10^{-3})^2 = 1.44\times10^{-6}$ (scientific notation on)

Common uses

Math & science: simplify expressions, check homework, evaluate exponential models.
Engineering: power laws, scaling, orders of magnitude.
Finance: growth rates, compounding approximations (with rounding control).
Data work: normalize values using roots (e.g., square-root transforms)

Notes & limitations

Even roots of negative bases (e.g., $8)^{1/2}$ ) are not real and are flagged.
Decimal exponents use standard floating-point math, then your chosen rounding mode is applied for a clean result.
For exact integer powers, we use high-precision integer arithmetic to avoid rounding errors.

FAQs

Q: What exponents can I enter?
Integers (…−3, −2, −1, 0, 1, 2, 3…), decimals (e.g., 0.5, 2.75), and fractions like p/q (e.g., 1/2, 3/4).

Q: How do I do roots?
Enter the exponent as a fraction: 1/2 for square root, 1/3 for cube root, p/q for the q-th root of $a^p$ .

Q: Can I use negative exponents?
Yes. $a^{-n} = 1/a^n$ . For example, $2^{-3} = 1/8 = 0.125$ .

Q: Why do I see scientific notation?
Toggle Scientific notation if results are very large/small. You can switch it off to see a standard decimal form.

Q: What do the rounding modes mean?

Half Up: .5 goes up
Half Even (banker’s): .5 to nearest even
Half Away: .5 away from zero
Half Down: .5 goes down
Truncate/Floor/Ceil: directional rounding

Q: Why does $8)^{1/2}$ show an error?
Even roots of negative numbers are not real (complex). The tool warns instead of returning a complex value.

Q: Does the tool support scientific notation inputs?
Yes. You can type values like 1.23e-4 for the base.

Q: How accurate is the result?
Integer powers are done with exact integer math; other cases are rounded using your selected mode and decimal places.