Exponentiation (x^n) multiplies x by itself n times. It extends naturally to negative exponents (reciprocals), fractional exponents (roots), and zero (anything^0 = 1). Powers grow extremely fast — 2^10 = 1,024 but 2^20 = 1,048,576 and 2^64 ≈ 1.84 × 10^19.
How to Use
Enter base and exponent:
- Integer: 2^10 = 1024
- Negative: 2^-3 = 1/8 = 0.125
- Fractional: 27^(1/3) = 3 (cube root)
Exponent Rules
- x^0 = 1 (except 0^0 is debated)
- x^(-n) = 1/x^n
- x^(1/n) = ⁿ√x (nth root)
- x^a × x^b = x^(a+b)
- (x^a)^b = x^(a×b)
Special Cases
- 0^0: conventionally 1 in combinatorics
- Negative base with fractional exponent: complex result
- Powers of 2: fundamental in computing
Step-by-Step Instructions
- 1Enter the base number.
- 2Enter the exponent.
- 3View the result in standard and scientific notation.
- 4Check the step-by-step expansion.
- 5Try fractional exponents for roots.