Calculate any base raised to any power — including large exponents, negative exponents, and fractional (decimal) exponents.
This tool calculates the result of raising a number (the base) to a power (the exponent), including support for negative and fractional exponents. It's useful for algebra homework, scientific calculations, and understanding exponential growth or decay.
bⁿ means the base b multiplied by itself n times. For negative exponents: b⁻ⁿ = 1/bⁿ. For fractional exponents: b^(1/n) is equivalent to the nth root of b, so b^(1/2) is the square root of b.
Enter a base number and an exponent, and the calculator returns the result of the base raised to that power.
Example 1: 2⁵ = 2 × 2 × 2 × 2 × 2 = 32.
Example 2: 5⁻² = 1/5² = 1/25 = 0.04.
What does a negative exponent mean? A negative exponent means take the reciprocal of the base raised to the positive version of that exponent — for example, 2⁻³ = 1/2³ = 1/8.
What is any number raised to the power of 0? Any non-zero number raised to the power of 0 equals 1, a fundamental rule in exponent mathematics.
What does a fractional exponent mean? A fractional exponent represents a root — for example, x^(1/2) is the square root of x, and x^(1/3) is the cube root of x.
How are exponents used in real life? Exponents describe compound interest growth, population growth, radioactive decay, computer storage sizes (like kilobytes as 2^10 bytes), and many scientific measurements spanning very large or small scales.
What's the difference between 2³ and 3²? These give different results — 2³ = 8 (2 multiplied by itself 3 times), while 3² = 9 (3 multiplied by itself 2 times) — exponentiation is not commutative.