Exponent Calculator

Enter any two of base, exponent, and result to solve for the third — including fractional exponents.

What exponentiation means

an means multiplying the base a by itself n times. This calculator generalizes that to solve for whichever of the three values — base, exponent, or result — you don't already know, using logarithms and roots as needed.

Key exponent rules

Same-base multiplication adds exponents (an×am=an+m), same-base division subtracts them, and raising a power to another power multiplies them ((am)n=amn). A negative exponent means "take the reciprocal": a-n = 1/an. Any nonzero base raised to the power 0 equals 1.

This calculator works with real numbers only. Taking an even root of a negative number (like solving x²=-4 for x) requires an imaginary number, which isn't supported — you'll see "NAN" in that case.

Common questions

Can I enter a fractional exponent?

Yes — enter it in decimal form (0.5 instead of 1/2). A fractional exponent with numerator 1 is equivalent to taking a root: raising to the power 0.5 is the same as a square root.

Why can't I solve for the exponent with a negative base?

Logarithms are only defined for positive bases, so solving basex=result for x requires a positive base (and a positive result) — if you know the exponent and result already, solving for the base handles negative and fractional cases more flexibly instead.

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