Work out any power bⁿ, whether the exponent is a whole number, a negative or a fraction, or find the nth root of a number. Square roots of whole numbers are also shown in simplest radical form.
An exponent says how many times to multiply the base by itself: 2⁵ = 2 × 2 × 2 × 2 × 2 = 32. A negative exponent means "one over": 2⁻³ = 1 ÷ 2³ = 0.125. A fractional exponent is a root: 81/3 = ∛8 = 2, and 160.5 = √16 = 4. Anything (except 0) to the power 0 is 1.
The nth root of x is the number that, raised to the power n, gives x: ⁿ√x = x1/n. Even roots of negative numbers aren’t real numbers, but odd roots are: ∛(−27) = −3.
A square root is in simplest radical form when the number under the root has no square factors left. √72 = √(36 × 2) = 6√2, because 36 is the largest perfect square that divides 72.
It means the reciprocal: b⁻ⁿ = 1 ÷ bⁿ. So 10⁻² = 1/100 = 0.01 and 5⁻¹ = 0.2.
The denominator is a root and the numerator is a power: b^(m/n) = (ⁿ√b)^m. For example 8^(2/3) = (∛8)² = 2² = 4.
By convention in algebra, combinatorics and most calculators, 0⁰ = 1. Some areas of analysis leave it undefined, but 1 is the standard value.
Find the largest perfect square that divides the number, take its root outside, and leave the rest inside: √50 = √(25 × 2) = 5√2.
Not in real numbers. √(−9) = 3i, an imaginary number. Odd roots are fine: ∛(−8) = −2, and this calculator handles those.
