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Exponent Calculator
Our free exponent calculator raises any base to any power — whole numbers, negative exponents, and fractional exponents included. Enter a base and an exponent and you get the answer instantly, with the step shown in plain language, so you can see exactly how the result was reached.
Try 2^10, 9^0.5, or 2^-3. The base is the number being multiplied; the exponent says how many times.
| Base | 2 |
| Exponent | 10 |
| Step | Repeated multiplication |
| Result | 1,024 |
How it works
An exponent is shorthand for repeated multiplication. Writing 2^10 is much shorter than writing 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2, but it means exactly the same thing: start with 2 and multiply by 2 ten times. The number at the bottom, the base, is what gets multiplied. The small number up top, the exponent or power, says how many times. So 3^4 is 3 × 3 × 3 × 3 = 81, and 10^3 is 10 × 10 × 10 = 1,000.
Exponents also work when the exponent is not a counting number. A negative exponent flips the power into a fraction: a^−n = 1 ÷ a^n. That is why 2^−3 = 1 ÷ 8 = 0.125 — the negative sign does not make the answer negative, it turns the multiplication into a division. A fractional exponent means a root: an exponent of 1/2 is a square root, so 9^0.5 = 3 because 3 × 3 = 9, and an exponent of 1/3 is a cube root, so 27^(1/3) = 3. The calculator handles both cases and explains which rule it used.
A few rules make exponents easier to work with by hand. Any non-zero number to the power of 0 is 1 — 5^0 = 1, 100^0 = 1 — because you have multiplied by the base zero times, leaving the starting value of 1. Any number to the power of 1 is itself. When you multiply powers with the same base, you add the exponents: 2^3 × 2^4 = 2^7. When you raise a power to another power, you multiply the exponents: (2^3)^2 = 2^6 = 64. These rules are what let scientists and engineers work with very large and very small numbers without writing out dozens of zeros.
Exponents run a surprising amount of American life. Compound interest grows by a power: $1,000 at 7% a year for 10 years is $1,000 × 1.07^10, about $1,967. A virus or a viral video spreads by powers, doubling again and again. Computer memory is built on powers of 2, which is why 2^10 = 1,024 is the number behind the kilobyte. Even the Richter scale for earthquakes is exponential — a magnitude 6 quake is about ten times stronger than a magnitude 5, not just one unit stronger.
Worked example
A computer technician in California is explaining why storage sizes jump the way they do, and asks: what is 2 to the power of 10? Enter base 2 and exponent 10 in the calculator above.
Step 1 — write out the repeated multiplication: 2^10 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2. Step 2 — build it up in pairs: 2 × 2 = 4, 4 × 2 = 8, 8 × 2 = 16, 16 × 2 = 32, 32 × 2 = 64, 64 × 2 = 128, 128 × 2 = 256, 256 × 2 = 512, 512 × 2 = 1,024. The answer is 1,024, and the calculator shows the same result: 2^10 = 1,024.
Two more quick checks show the other rules at work. With base 9 and exponent 0.5, the calculator gives 3, because 9^0.5 is the square root of 9. With base 2 and exponent −3, it gives 0.125, because 2^−3 = 1 ÷ 2^3 = 1 ÷ 8. Try all three in the calculator and watch the step line change to match each rule.
FAQ
What is 2 to the power of 10?
2 to the power of 10 is 1024. It means 2 multiplied by itself 10 times: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 1024. This is why a kilobyte in computing is 1024 bytes.
What does a negative exponent mean?
A negative exponent means one divided by the same power with a positive exponent: a to the power of -n equals 1 divided by a to the power of n. For example, 2^-3 = 1 / (2^3) = 1/8 = 0.125.
What does a fractional exponent mean?
A fractional exponent means a root. An exponent of 1/2 is a square root, so 9^0.5 = 3, and an exponent of 1/3 is a cube root, so 27^(1/3) = 3. In general, a^(m/n) is the nth root of a raised to the m power.
What is any number to the power of 0?
Any non-zero number to the power of 0 is 1. For example, 5^0 = 1 and 100^0 = 1. Zero to the power of zero is undefined in most contexts, so this calculator does not give an answer for 0^0.
What is the difference between 2^3 and 3^2?
They are different because the base and the exponent play different roles. 2^3 means 2 x 2 x 2 = 8, while 3^2 means 3 x 3 = 9. Swapping the base and the exponent usually changes the answer, so always check which number is the base.