Exponent Calculator

How exponents work

An exponent says how many times to multiply a number by itself. 2^5 is 2 x 2 x 2 x 2 x 2 = 32. The small raised number is the exponent and the number being multiplied is the base.

The rules worth remembering

• Anything to the power of 0 is 1, so 7^0 = 1.
• A negative exponent flips it: 2^-3 = 1/8 = 0.125.
• A fractional exponent is a root: 9^(1/2) = 3 and 27^(1/3) = 3.
• When you multiply the same base, add the exponents: 2^3 x 2^4 = 2^7.
• When you raise a power to a power, multiply: (2^3)^2 = 2^6.

Where you will meet them

Compound interest, population growth, computer memory (2^10 = 1,024) and scientific notation all rely on exponents. Doubling every year for 10 years is 2^10, a factor of 1,024.

When the calculator refuses

Zero cannot be raised to a negative power because that means dividing by zero. A negative base with a fractional exponent, like (-8)^0.5, has no real answer. Very large results are cut off rather than shown as "Infinity".

Examples to check

Type these into the calculator above to see how it behaves. Every result below was produced by the same calculator code that runs on this page.