Raise any number to any power, including negative and fractional exponents
💡 Why This Matters Exponents power everything from compound interest to computer science (binary, algorithm complexity) to scientific notation. This tool handles the full range — positive, negative, and fractional powers — so you're not stuck doing repeated multiplication by hand.
A single grain of rice doubled 63 times (2⁶³, the classic "chessboard" problem) comes out to over 9 quintillion grains — more rice than has ever existed on Earth. That's the power of exponential growth.
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An exponent tells you how many times to multiply a base number by itself. 2⁴ means 2 × 2 × 2 × 2 = 16. This calculator generalizes beyond whole-number exponents: negative exponents flip the base into a fraction (2⁻⁴ = 1/16), and fractional exponents compute roots (2^0.5 is the same as √2). Under the hood it's all one operation, base^exponent, applied consistently across the whole range.
A positive exponent greater than 1 gives you growth — the result is bigger than the base. An exponent between 0 and 1 gives you a root, so the result shrinks toward 1. A negative exponent always produces a fraction (or decimal) less than 1, unless the base itself is a fraction, in which case it flips the relationship. Any nonzero base raised to the 0 power always equals exactly 1.
Negative bases combined with fractional exponents often don't have a real-number answer — the same issue as taking an even root of a negative number — and this calculator will flag that case rather than silently return a wrong result. Very large exponents can produce numbers your browser displays in scientific notation, and floating-point rounding means results with many decimal places may show tiny imprecision at the far right digits.
Exponents show up in compound interest, population growth models, computer memory (powers of 2), earthquake magnitude (powers of 10), and pH scales. Try a few whole-number powers first to build intuition, then experiment with negative or fractional exponents to see how they behave differently.
Example: Say your base is 5 and your exponent is -2. That means 5⁻² = 1 ÷ 5² = 1 ÷ 25 = 0.04. Plugging base 5 and exponent -2 into this calculator gives you that same 0.04 directly, no manual reciprocal step needed.
A negative exponent means take the reciprocal of the base raised to the positive version of that exponent. For example, 2⁻³ = 1 ÷ 2³ = 1 ÷ 8 = 0.125.
Any nonzero number raised to the power of 0 equals 1. This holds by definition so the rules of exponents stay consistent — for example, 5² ÷ 5² = 5⁰, and anything divided by itself is 1.
Yes — a fractional exponent represents a root. For example, x^(1/2) is the square root of x, and x^(1/3) is the cube root. This calculator accepts decimal exponents like 0.5 to compute these.
It often has no real-number answer, the same way an even root of a negative number doesn't. This calculator will flag that case rather than return an incorrect number.