Math
Power of a Number Calculator
Most calculators give up on 2^100 and show 1.2676506e30.
This one shows all 31 digits, 1,267,650,600,228,229,401,496,703,205,376, exactly. Fractions and decimals work too: (3/4)^-2 is exactly 16/9, 8^(2/3) is exactly 4, and irrational results like 2^0.5 get a 12-place decimal with scientific notation.
Whole number, decimal, or fraction. Negatives allowed.
Whole number, decimal, or fraction like 2/3.
Try an example
Result
a^b
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- Scientific notation
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- Size
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- Type
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Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What a power means
The The number being raised to a power, or the side a shape's height is measured from. is the number being multiplied and the The small raised number saying how many times to multiply the base by itself. counts the factors. Negative exponents flip to The number you get by flipping a fraction; 3/4 becomes 4/3, and 5 becomes 1/5., a zero exponent gives 1, and a fractional exponent p/q takes a q-th root and then a p-th power.
Why exact digits matter
Floating-point arithmetic keeps only about 16 significant digits, so 2^100 in a spreadsheet is really 1.2676506002282294 × 10^30 with the rest lost. This calculator uses arbitrary-precision integers, so 2^1000 (302 digits) or 7^5000 (4,226 digits) come out with every digit correct, plus a digit count and scientific form for scale.
Quick reference
| Power | Value |
|---|---|
| 2^10 | 1,024 |
| 2^32 | 4,294,967,296 |
| 2^64 | 18,446,744,073,709,551,616 |
| 10^-3 | 1/1000 = 0.001 |
| (2/3)^3 | 8/27 ≈ 0.296296 |
| 8^(2/3) | 4 |
| (-2)^5 | -32 |
| 2^0.5 | 1.414213562373… |
How to use this calculator
- Type the base: a whole number, decimal, or fraction such as 3/4.
- Type the exponent: whole, negative, decimal, or a fraction like 2/3.
- Read the exact value; huge integers show the digit count and scientific form up top and all digits in the scrollable box.
Common mistakes and edge cases
- (-2)^2 = 4 but -2^2 = -4. Type the base as -2 to square the negative number.
- A negative base with an even-root exponent like (-4)^(1/2) is not a real number.
- 0^0 is indeterminate and 0 to a negative power divides by zero; both are reported as undefined.
- A decimal exponent like 0.333 is not 1/3. Type 1/3 for an exact cube root.
Worked examples
2^100
All 31 digits
a^b
1,267,650,600,228,229,401,496,703,205,376
2^1000
302 digits, shown in scientific form up top
a^b
1.0715086 × 10^301
Negative exponent
(3/4)^-2 = 16/9
a^b
16/9
Fractional exponent, exact
8^(2/3) = 4
a^b
4
Irrational
2^0.5 = √2
a^b
1.4142135624
Negative base
(-2)^5 = -32
a^b
-32
Decimal base
1.5^3 = 27/8
a^b
27/8
Zero exponent
Anything nonzero to the 0 is 1
a^b
1
Not real
(-4)^(1/2)
a^b
—
Undefined
0^-1
a^b
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Frequently asked questions
What is 2 to the power of 100?+
1,267,650,600,228,229,401,496,703,205,376, about 1.27 × 10^30. It has 31 digits.
How many digits does 2^1000 have?+
302 digits. In general 2^n has floor(n × log₁₀ 2) + 1 = floor(0.30103 n) + 1 digits.
How do I calculate a fraction raised to a power?+
Raise the numerator and denominator separately: (3/4)^2 = 9/16. A negative exponent flips the fraction first: (3/4)^-2 = (4/3)^2 = 16/9.
What does a fractional exponent mean?+
a^(p/q) is the q-th root of a raised to the p-th power. 8^(2/3) = (cube root of 8)^2 = 2^2 = 4.
Why is (-4)^(1/2) undefined?+
It asks for a square root of a negative number, which is not a real number. Odd roots of negatives are fine: (-8)^(1/3) = -2.
What is the largest power this calculator can show exactly?+
Results up to 20,000 digits are shown with every digit. Beyond that it falls back to a floating-point value, and above about 10^308 it reports the number as too large.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026