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About this tool
Raise any number to any power, including negative and fractional exponents, with exact big-integer and fraction answers, scientific notation and steps.
This exponent calculator raises a base to any power and keeps the answer exact whenever it can. Whole-number powers are computed with JavaScript BigInt by repeated squaring, so 2^64 = 18,446,744,073,709,551,616 and 7^1000 are shown digit for digit (up to 100,000 digits). Bases can be decimals, fractions or e-notation such as 6.02e23, and each is converted to an exact fraction first, so (2/3)^−3 = 27/8. Fractional exponents are treated as roots — 27^(2/3) is the cube root of 27, squared — with an exact answer when the root is whole and a simplified radical such as 8^(1/2) = 2√2 otherwise. Results come with scientific and E notation, the working, and a laws-of-exponents checker.
Open Exponent Calculator on AltFTool — it loads instantly in your browser.
Type the Base (a) — a whole number, decimal, fraction like 3/4, or e-notation like 6.02e23.
Type the Exponent (b) — such as 10, -2, 0.5 or 2/3 — or tap a quick button: x², x³, x⁻¹, x^½ or x^⅓.
Read the exact result, its scientific and E notation, digit count and decimal value, and follow each step in the Working card.
Copy the answer, download huge results as a .txt file, or test the laws of exponents with your own a, m and n.
Integer and fraction results are computed with whole-number arithmetic, so even hundreds of digits are correct to the last one. Very large results can be downloaded as a .txt file.
Positive, zero, negative, decimal and fractional exponents all work, including odd roots of negative numbers (−27)^(1/3) = −3. Even roots of negatives return the principal complex value.
The working names the step — a⁻ⁿ = 1/aⁿ, a^(m/n) = (ⁿ√a)ᵐ or (p/q)ⁿ = pⁿ/qⁿ — and expands small powers such as 3⁴ = 3 × 3 × 3 × 3.
Enter a, m and n to see the product, quotient, power, zero, negative and fractional exponent rules evaluated on both sides with your own numbers.
| Power | Value | Where you meet it |
|---|---|---|
| 2⁰ | 1 | |
| 2¹ | 2 | |
| 2² | 4 | |
| 2³ | 8 | bits in a byte |
| 2⁴ | 16 | |
| 2⁵ | 32 | |
| 2⁶ | 64 | |
| 2⁷ | 128 | |
| 2⁸ | 256 | values one byte can hold |
| 2⁹ | 512 | |
| 2¹⁰ | 1,024 | bytes in 1 KiB (kibibyte) |
| 2¹¹ | 2,048 | |
| 2¹² | 4,096 | |
| 2¹³ | 8,192 | |
| 2¹⁴ | 16,384 | |
| 2¹⁵ | 32,768 | |
| 2¹⁶ | 65,536 | values a 16-bit number can hold |
| 2¹⁷ | 131,072 | |
| 2¹⁸ | 262,144 | |
| 2¹⁹ | 524,288 | |
| 2²⁰ | 1,048,576 | bytes in 1 MiB (mebibyte) |
Each power of 2 is double the one before. 2¹⁰ = 1,024 is why a kibibyte is 1,024 bytes rather than 1,000. Enter any exponent above for larger powers.
An exponent says how many times to multiply the base by itself: aⁿ = a × a × … × a with n copies of a. So 2⁵ = 2 × 2 × 2 × 2 × 2 = 32. For large exponents it is faster to square repeatedly — 2⁸ = ((2²)²)² — which is the method this calculator uses internally.
A negative exponent means take the reciprocal: a⁻ⁿ = 1 / aⁿ. For example 2⁻³ = 1 / 2³ = 1/8 = 0.125, and 10⁻³ = 0.001. It does not make the answer negative. A negative exponent on a fraction flips it: (2/3)⁻² = (3/2)² = 9/4.
A fractional exponent is a root. a^(1/n) is the nth root of a, and a^(m/n) is that root raised to the power m. So 8^(1/3) = 2 and 27^(2/3) = (∛27)² = 3² = 9. A decimal exponent such as 0.5 is the same as 1/2, a square root.
Any non-zero number to the power 0 equals 1. This follows from the quotient rule: aⁿ ÷ aⁿ = aⁿ⁻ⁿ = a⁰, and anything divided by itself is 1. The case 0⁰ is usually defined as 1 in algebra and combinatorics, which is what this calculator returns, with a note.
The main rules are: aᵐ · aⁿ = aᵐ⁺ⁿ (product), aᵐ ÷ aⁿ = aᵐ⁻ⁿ (quotient), (aᵐ)ⁿ = aᵐⁿ (power of a power), (ab)ⁿ = aⁿbⁿ, (a/b)ⁿ = aⁿ/bⁿ, a⁰ = 1, a⁻ⁿ = 1/aⁿ and a^(m/n) = ⁿ√(aᵐ). The checker on this page evaluates both sides of each rule with your numbers.
With a whole-number exponent, the sign depends on whether the exponent is even or odd: (−2)⁴ = 16 but (−2)³ = −8. Brackets matter — −2⁴ means −(2⁴) = −16. With a fractional exponent, odd roots of negatives are real, (−8)^(1/3) = −2, while even roots like (−4)^(1/2) are not real numbers.
2⁶⁴ = 18,446,744,073,709,551,616, a 20-digit number. One less than this, 2⁶⁴ − 1, is the largest value an unsigned 64-bit integer can store. The calculator gives the exact value of any power of 2, along with its scientific notation, 1.84467440737 × 10¹⁹.
Scientific notation writes a number as m × 10ᵏ with 1 ≤ m < 10. The exponent k is one less than the number of digits for a whole number, so 1,024 = 1.024 × 10³. E notation writes the same thing as 1.024e+3, the format used by spreadsheets and programming languages. Both are shown with every result.
The number of digits in aⁿ is ⌊n · log₁₀ a⌋ + 1. For 2¹⁰⁰ that is ⌊100 × 0.30103⌋ + 1 = 31 digits, and 7¹⁰⁰⁰ has 846 digits. The calculator counts digits exactly for results up to 100,000 digits and switches to scientific notation beyond that.
In aⁿ, a is the base and n is the exponent (or index); the whole expression, or its value, is called the power. So in 3⁴ = 81, 3 is the base, 4 is the exponent, and 81 is the fourth power of 3. People often use “power” and “exponent” interchangeably.
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