Exponent Calculator

What is an exponent?

An exponent tells you how many times to multiply a base by itself. In x^y, x is the base and y is the exponent (power). Exponents let you express very large or small numbers compactly, simplify algebra, and model growth and decay in science, engineering, and finance.

Core rules of exponents

• Product rule: x^a · x^b = x^(a+b)
• Quotient rule: x^a ÷ x^b = x^(a−b), x ≠ 0
• Power rule: (x^a)^b = x^(ab)
• Zero exponent: x^0 = 1 for x ≠ 0
• Negative exponent: x^(−n) = 1 / x^n for x ≠ 0
• Fractional exponent: x^(p/q) = q-th root of x^p, defined for x ≥ 0 when q is even

Supported inputs and formats

• Integers and decimals: Works with positive and negative bases/exponents.
• Fractions: Enter exponents like 1/2, -3/4, or 5/2 to represent roots and rational powers.
• Scientific notation: Use forms like 6.02e23 or 3.2E-5 for convenience.

Examples

• 3^4: 3 × 3 × 3 × 3 = 81
• 2^(−3): 1 / 2^3 = 1/8 = 0.125
• 9^(1/2): √9 = 3
• 27^(2/3): (³√27)^2 = 3^2 = 9
• 10^6: 1,000,000 (scientific: 1×10^6)

Common pitfalls

• 0^0: Undefined in this calculator.
• Negative base with non-integer exponent: May be complex; the calculator returns a real result only when defined.
• Even roots of negatives: Not real numbers (e.g., (−4)^(1/2)).
• Order of operations: Exponentiation precedes multiplication/division unless parentheses indicate otherwise.

Who uses this exponent calculator?

• Students: Algebra, precalculus, scientific notation, and problem sets.
• Professionals: Engineering scaling laws, signal processing (dB), and compounding.
• Researchers: Modeling exponential growth/decay, power laws, and data transformations.
• Educators: Teaching exponent properties and root relationships.

Frequently asked questions

HOW TO calculate x^y online?

Enter the base x and exponent y, select precision and format, and click Calculate. The result and steps appear instantly.

HOW TO enter fractional exponents like 1/2 or -3/4?

Type them as fractions in the exponent field (e.g., 1/2 for square root). The calculator interprets p/q as a rational exponent.

HOW TO handle negative exponents?

Use the minus sign in the exponent (e.g., x^-3). The result equals 1 divided by x^3, provided x ≠ 0.

HOW TO compute powers with scientific notation?

Enter numbers like 6.02e23. The tool parses e/E notation and applies exponent rules before formatting the output.

HOW TO deal with negative bases and fractional exponents?

If the reduced denominator of the fraction is even, the real result doesn’t exist (it would be complex). The calculator shows a warning.

HOW TO use modulus x^y mod m?

Check “Use modulus” and enter an integer m > 1. The calculator uses fast modular exponentiation for integer x, y.

HOW TO fix overflow or very large outputs?

Switch the result format to Scientific or Engineering and reduce decimals. Auto chooses a readable format automatically.