Calculate exponents and solve for base, exponent, or result
Enter values into any two of the input fields to solve for the third.
Exponentiation is a mathematical operation, written as an, involving two numbers: the base a and the exponent (or power) n.
When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, an is the product of multiplying n bases:
an = a × a × ... × a
(n times)
Note: The calculator accepts negative bases but will return "NAN" for imaginary numbers. Fractional exponents are supported if entered in decimal form (e.g., 0.5 for 1/2).
an × am = a(n+m)
EX:
2² × 2⁴ = 4 × 16 = 64
2² × 2⁴ = 2(2+4) = 2⁶ = 64
a(-n) = 1 / an
EX:
2(-3) = 1 / (2 × 2 × 2) = 1/8
am / an = a(m-n)
EX:
2² / 2⁴ = 4 / 16 = 1/4
2² / 2⁴ = 2(2-4) = 2(-2) = 1/4
(am)n = a(m × n)
EX:
(2²)⁴ = 4⁴ = 256
(2²)⁴ = 2(2×4) = 2⁸ = 256
(a × b)n = an × bn
EX:
(2 × 4)² = 8² = 64
(2 × 4)² = 2² × 4² = 4 × 16 = 64
(a / b)n = an / bn
EX:
(2/5)² = 2² / 5² = 4/25
a1 = a
Any number raised to the power of 1 equals itself.
a0 = 1
Any number (except 0) raised to the power of 0 equals 1. There is debate about 0⁰, but using the multiplication rule (an × a0 = an), we can argue that a0 = 1 for all a.
a(1/n) = n√a
A fractional exponent represents a root. The calculator can handle fractional exponents (even when the numerator is not 1) if entered in decimal form.
EX:
3(2/5) = (3(1/5))² = (1.2457309399)² = 1.5518499999
When the base is negative and the exponent is a positive integer:
For fractional exponents of negative bases, the result involves imaginary numbers. The calculator returns "NAN" for such cases.
EX:
Compute: -2⁵ = -32 (negative base, odd exponent)
-2(1/2) = √(-2) = 1.414i (imaginary number, returns NAN)