Large Exponent Calculator
Three tools in one: exact big powers ab via BigInt (thousands of digits, with digit count and scientific notation), fast modular exponentiation ab mod m by square-and-multiply with a step table, and last digits / last-digit cycles of giant powers. Everything runs locally in your browser — no server, no limits, no signup.
Scope, stated plainly: this page computes powers and modular powers. It does not solve equations for an unknown exponent — for that (e.g. find x in 2x = 32) use our exponent equation solver.
Exact big power ab
Modular exponentiation ab mod m
Last digits of ab
How square-and-multiply works (worked example)
To compute 713 mod 100, read the exponent in binary — 13 = 11012 — then walk the bits from least significant up, squaring the base each step and multiplying it into the result only where the bit is 1:
| bit | value | base (squared mod 100) | action | result r |
|---|---|---|---|---|
| 0 | 1 | 7 | r = 1 × 7 = 7 | 7 |
| 1 | 0 | 49 | skip (bit is 0) | 7 |
| 2 | 1 | 1 | r = 7 × 1 = 7 | 7 |
| 3 | 1 | 1 | r = 7 × 1 = 7 | 7 |
FAQ
What is 2^100?
2^100 = 1267650600228229401496703205376 — a 31-digit number, about 1.26765 × 10^30. Try it in the Big Power tab: enter base 2 and exponent 100.
What is 2^1000?
2^1000 is a 302-digit number, about 1.07150 × 10^301. It is far beyond what a normal calculator or spreadsheet can hold exactly — this page computes it digit-for-digit with BigInt.
What is 7^13 mod 100?
7^13 mod 100 = 7. Square-and-multiply does it in 4 steps (13 in binary is 1101): square the base each bit, multiply into the result only on 1-bits.
What is 3^5 mod 7?
3^5 mod 7 = 5, since 3^5 = 243 and 243 mod 7 = 5.
What are the last 5 digits of 2^100?
The last 5 digits of 2^100 are 05376. Enter base 2, exponent 100, k = 5 in the Last Digits tab.
What is the last digit of 2^100?
The last digit of 2^100 is 6. The last digits of powers of 2 cycle every 4: 2, 4, 8, 6 — and since 100 mod 4 = 0, the answer is the 4th of the cycle, 6.
Why is 123456789^987654321 mod 1000000007 computable instantly?
Because of square-and-multiply. The exponent 987654321 is about 2^30, so only ~30 squarings and ~30 conditional multiplications are needed — the whole thing finishes in microseconds. The answer is 652541198. (1000000007 is the famous prime modulus used in competitive programming.)
What is 0^0?
This calculator follows the standard computing convention 0^0 = 1 (as in JavaScript, Python, and most CAS tools). In pure mathematics the expression is sometimes treated as indeterminate — for counting and power-series contexts, 1 is the useful value.
Is this the same as an exponent equation solver?
No. This page computes a^b and a^b mod m for known a, b, m. If instead you need to solve for an unknown — e.g. find x such that 2^x = 32 — use our exponent equation solver, which finds exponents, bases, and verifies solutions by plugging them back in.
Free tool by NRTechStudio