NumberTally Exponent Calculator
Raise any base to any power — whole, negative, or fractional exponents — and see every step of the working, a powers comparison table, and a growth chart. Results update instantly. Free, no sign-up.
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Powers 1–10 of this base are compared below.
How Exponents Work
An exponent tells you how many times to multiply the base by itself: 210 means 2 × 2 × … × 2, ten times. Negative exponents flip the result into a fraction — 2−2 = 1 / 22 = 0.25 — and fractional exponents are roots in disguise: 91/2 is the square root of 9, which is 3.
Exponents grow astonishingly fast. That is why the powers table below is so useful: each extra power of 2 doubles the last, so 210 = 1,024 but 220 is already over a million. The chart uses a logarithmic scale so you can see every step.
Exponents in the Real World
Compound interest, population growth, viral spread, and radioactive decay all run on exponents. Computer memory is sized in powers of two (a kilobyte is 210 bytes), and scientific notation like 3 × 108 m/s for the speed of light is just exponent shorthand for very big and very small numbers.
Frequently Asked Questions
What does 2^10 mean?
It means 2 multiplied by itself 10 times: 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1,024.
What is a negative exponent?
A negative exponent means "one over" the positive power: 2−2 = 1 / 22 = 1/4 = 0.25.
What is a fractional exponent like 9^(1/2)?
A fractional exponent is a root: x1/n is the nth root of x, so 91/2 = √9 = 3 and 271/3 = ∛27 = 3.
What is 0^0?
It is indeterminate in mathematics — different approaches give different answers. This calculator reports it as 1 (the common computational convention) but flags it as undefined mathematically.
What are the basic exponent rules?
xa × xb = xa+b; xa / xb = xa−b; (xa)b = xab; x0 = 1 (for x ≠ 0).