About the Exponent calculator
This exponent calculator raises a base to any power. Whole-number exponents like 210, negative exponents like 5−2, fractional exponents like 82/3 and decimal exponents like 100.5 all work. You get the answer, the same value in scientific notation, and the number of digits in the whole-number part.
The working changes to match the problem: repeated multiplication for small whole powers, a reciprocal for negative powers, and a root followed by a power for fractions. It is a quick check for algebra homework, science calculations and growth problems.
How to use it
- Enter the number being multiplied in Base.
- Enter the power in Exponent. You can type a fraction such as
2/3or a decimal such as0.5. - Read the result and its scientific-notation form.
- Follow the step to see how the power was worked out.
The formula
An exponent says how many times to multiply the base by itself:
bn = b × b × … × b (n times)
- Negative exponents mean a reciprocal:
b−n = 1 ÷ bn, so 2−3 = 1/8 = 0.125. - Fractional exponents mean roots:
bp/q = (q√b)p, so 82/3 = (∛8)² = 2² = 4. - Zero exponent:
b0 = 1for any non-zero b. - Decimal exponents follow
bx = ex·ln b, so 100.5 ≈ 3.1623.
A negative base with a fractional exponent is only real when the root is odd: (−8)1/3 = −2, but (−8)1/2 is not a real number.
The laws of exponents
A handful of rules lets you simplify almost any power by hand. They hold for any base b ≠ 0:
- Product rule:
bm × bn = bm+n, e.g. 2³ × 2⁴ = 2⁷ = 128. - Quotient rule:
bm ÷ bn = bm−n, e.g. 5⁶ ÷ 5⁴ = 5² = 25. - Power of a power:
(bm)n = bmn, e.g. (3²)³ = 3⁶ = 729. - Power of a product:
(ab)n = anbn.
These rules explain why b0 = 1: bn ÷ bn is 1, and the quotient rule says it is also bn−n = b0.
Exponents in real life and common slips
Exponents describe anything that grows or shrinks by the same factor again and again. Money growing at 5% a year for 10 years is multiplied by 1.0510 ≈ 1.629, which the compound interest calculator builds on. Computer memory comes in powers of two: 210 = 1,024.
Two slips are common. First, −3² is −9, because the power applies before the minus sign; to square −3, enter −3 as the base and get 9. Second, a negative exponent does not make the answer negative: 4−2 = 1/16 = 0.0625, a small positive number.
Frequently asked questions
How do you calculate a negative exponent?
Take the reciprocal of the positive power. For example, 10−3 = 1 ÷ 10³ = 0.001.
What does a fractional exponent mean?
The bottom of the fraction is a root and the top is a power. So 163/4 = (4√16)³ = 2³ = 8.
What is any number to the power of 0?
Any non-zero number to the power 0 is 1. By convention, the calculator also returns 1 for 00.
Why do I get an error with a negative base?
A negative base with an exponent like 1/2 or 0.5 would need the square root of a negative number, which is not a real number. Odd roots such as 1/3 are fine.
How big is 2 to the power of 100?
2100 is about 1.2677 × 1030, a 31-digit number. The calculator shows the digit count for large results.
Last updated October 24, 2026. Results are estimates for education and planning — see our disclaimer.