Exponent Calculator

Calculate powers, exponents, square roots, cube roots, and any nth root. Support for positive, negative, and fractional exponents.

Base (Number)

Exponent (Power)

Calculation Type

Exponent Result

Result

calculated value

Scientific Notation

e format

📐 Details:
Base: -
Exponent: -
Calculation: -

How to use the Exponent Calculator

Enter the base number.
Enter the exponent (not needed for square or cube root).
Choose the calculation type.
The result updates instantly in decimal and scientific notation.

Formula used

xⁿ = x × x × … (n times) x⁻ⁿ = 1 ÷ xⁿ ⁿ√x = x^1/n

Worked example

Examples

2¹⁰ = 1,024

5⁻² = 1 ÷ 25 = 0.04

√144 = 12; ∛27 = 3

4th root of 81 = 3

Laws of exponents

Multiplying powers with the same base adds the exponents (a^m × aⁿ = a^m+n); dividing subtracts them; a power of a power multiplies them ((a^m)ⁿ = a^mn). Any non-zero number to the power 0 equals 1. Exponents appear in compound interest, population growth, computer memory (2¹⁰ = 1,024) and scientific notation such as 3 × 10⁸ m/s for the speed of light.

Tips for accurate results

Fractional exponents are roots: x^0.5 = √x.
Even roots of negative numbers are not real numbers.
Very large results are easier to read in scientific notation.

Frequently Asked Questions

The reciprocal: 2⁻³ = 1/8.

1, except 0⁰, which is undefined in many contexts.

Choose Cube Root and enter the number.

Related Calculators

Content reviewed by Vinod, Easy Smart Calculator · Last updated October 2026

Understanding Exponents

Exponent (Power): 2³ means 2 × 2 × 2 = 8. The small number (3) is the exponent.

Square Root: √9 = 3, because 3² = 9. Asks "what number multiplied by itself equals 9?"

Cube Root: ∛8 = 2, because 2³ = 8. The third root.

Negative Exponent: 2⁻² = 1/(2²) = 1/4 = 0.25

Fractional Exponent: 8^(1/3) = ∛8 = 2. The numerator is the power, denominator is the root.

Common Powers & Roots

2⁵ = 32 (powers of 2 are common in computing)
10³ = 1000 (powers of 10 used in scientific notation)
√4 = 2 (square root)
∛27 = 3 (cube root)
2⁻³ = 0.125 (negative exponent)

Real-World Applications

Compound interest calculations (finance)
Population growth modeling
Physics equations and calculations
Engineering and construction
Computer science (binary, powers of 2)