Exponent Calculator
Raise any base to any power - positive, negative, or fractional. Get the result plus the expanded form for small whole powers, and a clear note when the answer is not a real number.
- Free, no account
- No watermark
- No usage limit
About the Exponent Calculator
The cube root of -8 is -2. Simple, true, and the big free exponent calculators mostly can't tell you that. Type (-8)^(1/3) into the popular ones and you get an error, a blank NaN, or a flat refusal that they "don't do imaginary numbers." Except there's nothing imaginary about it. -2 cubed is -8, so -2 is a real, correct answer, and a calculator that won't give it to you is quietly giving up on a case it should handle.
That gap is why this one exists. It raises any base to any power, positive, negative, fractional, decimal, and it knows the difference between a negative-base case that has a real answer and one that genuinely doesn't. The whole thing runs in your browser, so nothing you type leaves your machine, and once the page loads it keeps working with no connection.
How to use
- Type the base in the first box, the number being raised. Positive, negative, or decimal all work, so
2,-8, and1.5are fine. - Type the exponent in the second box. Whole numbers (
10), negatives (-2), and decimals (0.5) are all valid. For a root, use the decimal form:0.5is a square root,0.3333333is a cube root. - Read the answer below. It updates as you type and shows the expression spelled out, like
2¹⁰ =, next to the result. - Check the expanded form. For small whole powers a dashed box writes out the multiplication,
2 · 2 · 2 · 2 · 2 = 32, so the number isn't just handed to you on faith. - Tap a preset in the
Try:row to watch it work, including the(-8)^⅓case that trips other tools.
The negative base problem, and why we nail it
A negative base behaves three different ways depending on the exponent, and only one of them is actually hard.
Whole powers are easy. (-2)^2 is (-2)(-2) = 4, positive, because two negatives cancel. (-2)^3 is -8, negative, because an odd count of them leaves one behind. An even power always lands positive. An odd one keeps the minus sign, and no calculator struggles with either.
The hard case is a fractional exponent on a negative base, and it splits two ways. An odd root, like the cube root (-8)^(1/3), has a real answer of -2, since (-2)^3 is -8. An even root, like the square root (-4)^0.5, has none, because no real number squared comes out negative. The reason so many tools botch this is that they lean on a single built-in power function that returns NaN for every fractional power of a negative, real answer or not. So they crash, or they play it safe and reject the whole category, which throws out the genuine cube roots along with the impossible square roots.
This calculator checks which case you're in first. When the exponent is an odd root it computes the real root by hand and gives you the number. When it's an even root of a negative it won't fake a value or spit out NaN, it says "Not a real number" and tells you the reason. So you get the actual answer whenever one exists, and a plain reason the rest of the time rather than a wrong number.
Fractional exponents are just roots
Once you see that a fraction in the exponent means a root, the rest clicks into place. x^(1/2) is the square root of x. x^(1/3) is the cube root. In general x^(1/n) is the nth root of x. So 16^0.5 = 4 and 27^(1/3) = 3. When the top of the fraction isn't 1 you do both steps: 8^(2/3) means cube-root 8 to get 2, then square that to get 4.
This tool takes the exponent as a single number, so a one-third power goes in as 0.3333333, not 1/3. More threes gets you closer to an exact cube root. The 27^⅓ preset does that conversion for you and lands on a clean 3. If you'd rather write 27^(1/3) literally with the real fraction, that's a job for the scientific calculator, which parses full expressions with parentheses. This one stays narrow on purpose, two boxes and one power, which is all you need most of the time.
Watch the parentheses: -4^2 is not (-4)^2
This one catches people before any calculator does. -4^2 and (-4)^2 give different answers. That's the order of operations, not a bug in the tool. Without parentheses the exponent binds tighter than the minus sign, so -4^2 reads as -(4^2) = -16. With parentheses, (-4)^2 squares the whole negative number and gives +16, the same digits with the opposite sign.
When you type -4 into the base box here, you're telling the tool the whole thing is negative, so it uses the (-4)^2 reading and returns 16. If you actually meant -(4^2), compute 4^2 and negate the result yourself. It's a small distinction that wrecks a lot of homework, so any time a minus sign sits next to a power, stop and check whether the parentheses are really where you think they are.
Frequently asked questions
Why doesn't a negative exponent make the answer negative?
Because a negative exponent means reciprocal, not negative result. 2^-2 is 1 / (2^2) = 1/4 = 0.25, a small positive number. The rule is x^-n = 1 / x^n, so the minus sign flips the value into a fraction instead of changing its sign. To get a negative answer you need a negative base raised to an odd power, not a negative exponent.
Why does this return 1 for 0^0?
Because that's the convention nearly all working math runs on. 0^0 is an indeterminate form, you can argue it toward 0 or toward 1 depending on how you approach it, but in combinatorics, algebra, and power series, defining it as 1 keeps the surrounding rules consistent. Some strict analysis courses leave it undefined instead, which is a deliberate choice on their part rather than a contradiction of this one.
When do I see something like 1.22e+14 instead of the whole number?
That's scientific notation, and on this tool it belongs to the decimal side. Once a decimal answer climbs past a trillion, twelve significant figures can no longer reach the ones place, so writing it out in full would mean filling the end with zeros nothing actually calculated. Rather than invent those digits it switches to 1.22264598056e+14, which reads as 1.22264598056 times 10 to the 14th. The same switch happens at the tiny end, below a billionth. Whole-number answers keep printing in full until they pass a thousand digits, and past that you get a four-figure reading like 4.024 × 10^2567 with the exact digit count beside it.
Are the big whole-number answers exact, or rounded?
Exact, to the last digit, however long they run. A whole base raised to a whole power skips ordinary decimal arithmetic entirely and multiplies with big integers, which carry no fixed digit limit. So 2^50 comes back as 1125899906842624 and not a tidied 1125899907000000, and 7^15 ends in 943 rather than a rounded 940. At sixteen and thirteen digits neither one looks rounded, which is exactly how a wrong tail slips past a reader unnoticed. Put a decimal anywhere, in the base or the exponent, and you are in floating-point territory instead, where roughly 15 digits is all the hardware carries. There the tool shows twelve and stops.
Can it give me an imaginary or complex answer?
No, it stays in real numbers on purpose. Ask for something like the square root of a negative and the honest answer is a complex number (2i for (-4)^0.5). Rather than display that, the tool flags the input as "Not a real number." Odd roots of negatives, which are real, it computes normally. For actual complex arithmetic you'd reach for a dedicated tool or a computer-algebra system.
Why did a power come back as a label instead of a number?
Two different things can do that, and they aren't the same problem. 0 raised to a negative power divides by zero, so there is genuinely no answer and you get "Undefined." A decimal answer past about 10^308 runs out of room in floating point, and that gets the same label because there is nothing usable left to hand back. Whole numbers don't hit that wall at all, so 10^400 returns all 401 of its digits. The one limit on that side is length. Past a hundred thousand digits the page stops before it builds the thing and tells you roughly how long the answer would have been, which is more useful than a frozen tab.