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Raise any base to any power, including negative and fractional exponents.
Raise any base to any power, including negative and fractional exponents.
Enter values above and click Calculate — results will appear here with the formula explained.
An exponent counts repeated multiplication: 2¹⁰ = 2×2×2×…×2 ten times = 1024. Exponents grow astonishingly fast — doubling at each step turns 10 doublings into a thousandfold increase.
Negative exponents express reciprocals, so 2⁻³ = 1/8. Fractional exponents express roots: 9^(1/2) = 3 and 27^(1/3) = 3. These rules let a single formula handle growth, decay, scaling and roots alike.
Laws of exponents compress whole calculation chains: x^a × x^b = x^(a+b), (x^a)^b = x^(ab), and (xy)^n = x^n × y^n. Simplifying 2^10 × 2^5 to 2^15 before computing avoids overflow and rounding error that direct multiplication invites.
Exponential growth versus linear growth is the intuition that matters: linear adds fixed amounts (100, 200, 300), exponential multiplies (100, 200, 400 at doubling). Compound interest, viral spread, Moore's-law transistor counts and pandemic curves all follow x^t — recognizing the shape early changes decisions that linear thinking gets catastrophically wrong.
Zero, one and negative bases are the edge cases: anything non-zero to power 0 is 1 (x^0 = 1 follows from x^n ÷ x^n), 0^0 is conventionally 1 in most calculators, negative bases with fractional exponents leave real numbers (use complex mode elsewhere), and 0 to a negative power is division by zero — undefined, which this calculator flags explicitly.
Floating-point limits bound real computation: results beyond ~1.8×10^308 overflow to Infinity (flagged here, not silently wrong), and fractional powers of large numbers lose low digits to rounding. For cryptographic or scientific magnitudes, dedicated big-number libraries beat browser doubles.
Raise any base to any power, including negative and fractional exponents. Formula: xⁿ means x multiplied by itself n times. Example: 2^10 = 1024.
An exponent counts repeated multiplication: 2¹⁰ = 2×2×2×…×2 ten times = 1024. Exponents grow astonishingly fast — doubling at each step turns 10 doublings into a thousandfold increase.
Negative exponents express reciprocals, so 2⁻³ = 1/8. Fractional exponents express roots: 9^(1/2) = 3 and 27^(1/3) = 3. These rules let a single formula handle growth, decay, scaling and roots alike.
Laws of exponents compress whole calculation chains: x^a × x^b = x^(a+b), (x^a)^b = x^(ab), and (xy)^n = x^n × y^n. Simplifying 2^10 × 2^5 to 2^15 before computing avoids overflow and rounding error that direct multiplication invites.
Exponential growth versus linear growth is the intuition that matters: linear adds fixed amounts (100, 200, 300), exponential multiplies (100, 200, 400 at doubling). Compound interest, viral spread, Moore's-law transistor counts and pandemic curves all follow x^t — recognizing the shape early changes decisions that linear thinking gets catastrophically wrong.
Zero, one and negative bases are the edge cases: anything non-zero to power 0 is 1 (x^0 = 1 follows from x^n ÷ x^n), 0^0 is conventionally 1 in most calculators, negative bases with fractional exponents leave real numbers (use complex mode elsewhere), and 0 to a negative power is division by zero — undefined, which this calculator flags explicitly.
Floating-point limits bound real computation: results beyond ~1.8×10^308 overflow to Infinity (flagged here, not silently wrong), and fractional powers of large numbers lose low digits to rounding. For cryptographic or scientific magnitudes, dedicated big-number libraries beat browser doubles.
2^10 = 1024. The same machinery gives 2^-10 = 1/1024 ≈ 0.00097656 and 16^(1/2) = 4. A growth check: $1,000 at 7% for 10 years is 1000 × 1.07^10 ≈ $1,967 — the exponent doing compound interest's work.
Formulas are standard public references (see our methodology). External standards are cited in the text where they apply.
Last reviewed: September 2026 · Report an error