Exponent Calculator
Calculate any base raised to any power. Handles large exponents, fractional powers (roots), and negative exponents.
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How to use this calculator
Raise the base to the given exponent. Fractional exponents represent roots: x^(1/n) = ⁿ√x.
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Enter the base number.
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Enter the exponent (power to raise the base to).
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Use fractional exponents for roots: 0.5 for square root, 0.333 for cube root.
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Use negative exponents for reciprocals: 2^(-3) = 1/8.
Frequently asked questions
What does a negative exponent mean?
A negative exponent means "take the reciprocal." 2^(-3) = 1/(2^3) = 1/8 = 0.125. 10^(-2) = 1/100 = 0.01. Negative exponents appear in scientific notation: 3.5 × 10^(-6) = 0.0000035.
What does a fractional exponent mean?
x^(1/n) = the nth root of x. x^(1/2) = √x; x^(1/3) = ∛x. More generally, x^(m/n) = (ⁿ√x)^m. So 8^(2/3) = (∛8)² = 2² = 4.
What is x^0?
Any non-zero base raised to the power 0 equals 1: x^0 = 1. This is consistent with the rule x^n / x^n = x^(n-n) = x^0 = 1. The value 0^0 is mathematically indeterminate, though it is often defined as 1 in combinatorics.
How do I calculate very large powers?
For very large exponents, results quickly become astronomical. 2^64 ≈ 1.84 × 10^19 (more than all grains of sand on Earth). At some point, the result exceeds JavaScript's floating-point precision and is shown in scientific notation.
Exponents and powers explained
Rules of exponents
x^a × x^b = x^(a+b); x^a / x^b = x^(a−b); (x^a)^b = x^(ab); (xy)^a = x^a × y^a; x^0 = 1; x^(-n) = 1/x^n; x^(1/n) = ⁿ√x. These rules are fundamental to algebra, calculus, and scientific notation.
Exponential growth in everyday life
Moore's Law: transistor counts doubled roughly every 2 years. COVID-19 early spread: exponential until interventions. Compound interest: exponential growth of money. Exponential functions grow faster than any polynomial — the fundamental insight behind why doubling times matter in epidemics and investment.
Scientific notation uses exponents of 10
Scientific notation expresses numbers as a × 10^n where 1 ≤ a < 10. Distance to Alpha Centauri: 4.07 × 10^13 km. Mass of a proton: 1.67 × 10^(-27) kg. This notation makes very large and small numbers readable and arithmetic on them practical.
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