Exponent Calculator
Calculate anything relating to exponents — from standard power and roots, to logarithms and scientific notation conversions.
Zero and Negative Rules
- Zero Exponent: Any non-zero number to the power of 0 is exactly 1 (e.g., x⁰ = 1).
- Negative Exponents: A negative exponent means to take the reciprocal of the positive exponent (e.g., x⁻² = 1 / x²).
- Fractional Exponents: Work as roots (e.g., x¹/² = √x).
Logarithm Fundamentals
- A logarithm answers the question: "To what power must the base be raised, to produce this number?"
- Natural Log (ln): Has the base $e$ (approx 2.718). Essential in calculus.
- Common Log (log): Has the base 10. Frequently used on scientific calculators.
Examples
Output: 256 (2 × 2 × 2 × 2 × 2 × 2 × 2 × 2)
Output: 0.001 (1 / 10³)
Output: 5 (The cube root of 125)
Output: 8 (Because 2⁸ = 256)
Frequently Asked Questions
What is scientific notation?
Scientific notation is a way of writing very large or very small numbers compactly. It represents a number as a decimal between 1 and 10 multiplied by a power of 10. For example 5,000,000 is written as 5 × 10⁶ or 5e+6. This calculator automatically shows scientific notation for answers over a million or under a ten-thousandth.
Why can't I calculate the even root of a negative number?
In the set of real numbers multiplying a number by itself an even number of times always gives a positive result. Therefore no real number multiplied by itself an even number of times can equal a negative number. The square root of -1 requires using imaginary numbers (denoted by "i").
What does a negative exponent mean?
A negative exponent means taking the reciprocal of the positive power. For instance 2⁻³ is the same as 1 / 2³. It basically means divide by the base that many times rather than multiply. Thus 2⁻³ = 1/8 or 0.125.
How does a logarithm work?
A logarithm is the inverse operation to exponentiation. While an exponent asks "what is 2 raised to the 8th power?" (Answer: 256), a logarithm asks "2 raised to what power equals 256?" (Answer: 8). Logarithms are incredibly useful for dealing with exponential growth scales like the Richter scale for earthquakes or decibels for sound.