Positive power
2^5 = 32.
Calculate powers, negative and fractional exponents, powers of ten, scientific notation, nth roots, and the missing exponent in a simple equation.
In a^b, a is the base and b is the exponent. A positive integer exponent tells how many times to multiply the base by itself.
Exponent rules also describe reciprocals, roots, powers of ten, and exponential equations.
Raise the base a to exponent b.
result = a^bA negative exponent produces the reciprocal, provided the base is nonzero.
a^-n = 1/a^nEven roots of negative values are not real numbers.
a^(1/n) = ⁿ√aFor a^x=y when a>0, a≠1, and y>0.
x = ln(y)/ln(a)2^5 = 32.
2^-3 = 1/2³ = 1/8 = 0.125.
9^(1/2) = √9 = 3, and 27^(1/3) = 3.
10^6 = 1,000,000.
For 2^x = 32, x = ln(32)/ln(2) = 5.
Integer bases and integer exponents use BigInt when the estimated exact output is at most 10,000 digits.
Complex-number results are outside this calculator's scope. Negative bases with fractional exponents are rejected in power mode.
Any nonzero base raised to zero equals 1. The expression 0^0 is treated as indeterminate because conventions differ by mathematical context. A zero base cannot have a negative exponent.
Scientific notation writes a number as a coefficient times 10 raised to an integer exponent. Normalized notation keeps one nonzero digit before the decimal point.
An nth root is an inverse power. Odd roots of negative numbers have real results, such as the cube root of −27 being −3; even roots do not.
It indicates the power to which a base is raised.
Any nonzero base raised to zero equals 1. This calculator treats 0^0 as indeterminate.
They produce reciprocals: a^-n equals 1 divided by a^n.
It represents a root or a combination of a root and power.
No. Inputs without real-number results receive a clear validation message.
The coefficient is adjusted to have one nonzero digit before the decimal point, with the power of ten changed accordingly.
For a positive base other than 1 and a positive target, use x=ln(y)/ln(a).
BigInt is used when the estimated result is no more than 10,000 digits.