Exponent Calculator
Calculate base raised to a power (bⁿ). Handles any real exponent including fractions and negatives.
Results update as you type.
How it works
Exponentiation is a mathematical operation where a base number is multiplied by itself a specified number of times. It is the third core operation built on repetition — addition repeats counting, multiplication repeats addition, and an exponent repeats multiplication. The expression b^n (read 'b to the power of n' or 'b raised to the nth power') means: multiply b by itself n times. Exponents follow important rules that make calculations easier: b^m × b^n = b^(m+n), (b^m)^n = b^(m×n), b^0 = 1 (for any non-zero b), b^(-n) = 1/b^n, and b^(1/n) = the nth root of b. Fractional exponents are particularly powerful: 4^(0.5) = √4 = 2, 8^(1/3) = ∛8 = 2, 32^(0.2) = ⁵√32 = 2. This connects exponentiation to roots. Exponents also tame very large and very small numbers through scientific notation, where a value is written as a number times a power of 10. Writing 300,000,000 as 3 × 10^8, or 0.0000004 as 4 × 10^(−7), keeps figures compact and readable across science and engineering. Exponential growth appears everywhere in nature and technology: compound interest, population growth, radioactive decay, and Moore's Law (the doubling of transistors roughly every 18 months). A firm grasp of exponents is essential for science, engineering, finance, and computer science.
bⁿ = b × b × b × ... (n times); b⁻ⁿ = 1/bⁿ; b^(1/n) = ⁿ√b
An exponent records repeated multiplication, so bⁿ simply means b used as a factor n times. The rules follow from that meaning: adding exponents combines repeated factors, and a zero exponent leaves an empty product of 1. A negative exponent inverts the result because it undoes multiplication, giving 1/bⁿ. A fractional exponent asks which number, multiplied by itself the denominator's number of times, rebuilds the base — that is a root.
Source:Standard mathematical definition
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter base (b) and exponent (n).
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Result (bⁿ) updates instantly as you type — no button to press.
Frequently asked questions
What is anything to the power of 0?
Any non-zero number raised to the power of 0 equals 1. This follows from the exponent rule b^n / b^n = b^(n−n) = b^0, and any number divided by itself is 1. So b^0 = 1 for any b ≠ 0. The expression 0^0 is mathematically indeterminate (it leads to conflicting values depending on how you approach it), but in many combinatorial contexts, it's defined as 1 for convenience. This rule is essential for polynomials and the binomial theorem.
How do negative exponents work?
A negative exponent means take the reciprocal of the positive exponent result: b^(-n) = 1/b^n. For example, 2^(-3) = 1/2^3 = 1/8 = 0.125. Negative exponents are not negative numbers — they represent fractions less than 1 (for bases greater than 1). This rule is fundamental in scientific notation: 10^(-3) = 0.001 (one thousandth). Negative exponents also appear in physics for units like m/s² = m × s^(-2).
What are fractional exponents?
Fractional exponents represent roots. The rule is b^(1/n) = the nth root of b, and b^(m/n) = (nth root of b)^m = nth root of b^m. For example: 4^(1/2) = √4 = 2; 8^(1/3) = ∛8 = 2; 16^(3/4) = (fourth root of 16)^3 = 2^3 = 8. This connects the exponent operation to root extraction and explains why square roots, cube roots, etc. are just special cases of exponentiation with fractional powers.
What is the difference between exponential growth and linear growth?
Linear growth adds the same amount each time (e.g., saving $100 per month: $100, $200, $300...). Exponential growth multiplies by the same factor each time (e.g., 10% compound interest: $1,000, $1,100, $1,210, $1,331...). In the short term, linear and exponential growth may look similar. Over time, exponential growth becomes enormously larger — this is why compound interest is so powerful, and why viral diseases spread so rapidly. Mathematically, any exponential eventually outpaces any polynomial (including linear).
What happens when you raise a negative number to a fractional exponent?
Raising a negative number to a fractional exponent with an even denominator produces a complex (imaginary) number in standard math, since you'd need to take an even root of a negative number. For example, (-4)^(1/2) = √(-4) = 2i (where i is the imaginary unit). For odd denominators, the result is real: (-8)^(1/3) = ∛(-8) = -2. Most calculators, including ours, return NaN (not a number) for cases that would yield complex results, since complex number support requires a different representation.