Raise a number to a power.
Result = b^n
The core formula for computing an exponent is straightforward. The base (b) is multiplied by itself a total of n times, where n is the exponent. This operation is called exponentiation and is written using superscript notation or the caret symbol (^).
For positive integer exponents this means repeated multiplication. The formula extends naturally to zero exponents (any non-zero base to the power of 0 equals 1), negative exponents (which produce reciprocals), and fractional exponents (which produce roots).
4^5 = 4 × 4 × 4 × 4 × 4 = 16 × 4 × 4 × 4 = 64 × 4 × 4 = 256 × 4 = 1,024
Result: 1,024
The result 1,024 means that 4 multiplied by itself 5 times equals 1,024. This is a straightforward positive-integer exponent. Notice how quickly the value grows — this illustrates exponential growth, where even a modest base can produce a large result with a relatively small exponent. If instead the exponent were negative, e.g., 4^(−5), the result would be the reciprocal: 1 ÷ 1,024 ≈ 0.000977.
Exponents are one of the most fundamental concepts in mathematics. The expression b^n (read as "b to the power of n") is a compact way of writing repeated multiplication.
| Rule | Formula | Example | |---|---|---| | Product Rule | b^m × b^n = b^(m+n) | 2^3 × 2^4 = 2^7 = 128 | | Quotient Rule | b^m ÷ b^n = b^(m−n) | 5^6 ÷ 5^2 = 5^4 = 625 | | Power Rule | (b^m)^n = b^(m×n) | (3^2)^4 = 3^8 = 6,561 | | Zero Exponent | b^0 = 1 (b ≠ 0) | 7^0 = 1 | | Negative Exponent | b^(−n) = 1 / b^n | 2^(−3) = 1/8 = 0.125 | | Fractional Exponent | b^(1/n) = ⁿ√b | 27^(1/3) = ∛27 = 3 |
2^10 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1,024. This value is well known in computing, where it represents one kilobyte (kibibyte) of binary data.
Break it into two steps: first take the cube root of 125, which is 5 (since 5^3 = 125), then square the result: 5^2 = 25. So 125^(2/3) = 25.
The two terms are often used interchangeably. Technically, in the expression b^n, the entire expression b^n can be called a 'power', while n is the 'exponent' and b is the 'base'. In everyday usage, saying '4 to the power of 3' and '4 with exponent 3' mean the same thing.
Logarithms are the inverse operation of exponentiation. If b^n = x, then log_b(x) = n. For example, since 2^8 = 256, we have log₂(256) = 8. Logarithms allow you to solve for an unknown exponent.
Yes. Expressions like 3^1.5 are valid. 3^1.5 = 3^(3/2) = (√3)^3 ≈ 5.196. Irrational exponents like 2^π ≈ 8.825 are also real numbers, computed using the identity b^x = e^(x · ln b).
An exponent is a number written as a superscript above and to the right of a base number. It tells you how many times to multiply the base by itself. For example, in 6^3, the base is 6 and the exponent is 3, meaning 6 × 6 × 6 = 216.
A negative exponent means you take the reciprocal of the base raised to the positive version of that exponent. For example, 5^(−2) = 1 / 5^2 = 1/25 = 0.04.
Yes. A negative base with an even exponent gives a positive result — for example, (−4)^2 = 16. A negative base with an odd exponent gives a negative result — for example, (−4)^3 = −64.
Any non-zero number raised to the power of 0 equals 1. This is a fundamental rule of exponents — for example, 99^0 = 1, (−7)^0 = 1, and (0.5)^0 = 1. The case 0^0 is considered indeterminate in pure mathematics.
A fractional exponent represents a root. Specifically, b^(1/n) equals the nth root of b. For example, 64^(1/2) = √64 = 8, and 8^(1/3) = ∛8 = 2. More generally, b^(m/n) = (ⁿ√b)^m.
This exponent calculator computes b^n for any base and power you enter. A scientific notation calculator specifically helps express very large or small numbers as a coefficient times a power of 10, and helps convert between standard and scientific notation forms.
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