Exponent Calculator
Calculate powers and exponents quickly and accurately. Enter a base and exponent to find the result.
What Is an Exponent?
Exponentiation is a mathematical operation written as an, where a is the base and n is the exponent.
When the exponent is a positive integer, exponentiation represents repeated multiplication of the base.
Basic Exponent Laws and Rules
an × am = an + m
am ÷ an = am − n
(am)n = am × n
(a × b)n = an × bn
a−n = 1 / an
a1 = a
a0 = 1
Fractional Exponents
A fractional exponent represents a root. For example, an exponent of 0.5 is equivalent to taking the square root.
Frequently Asked Questions
What is an exponent?
An exponent tells you how many times a number, called the base, is multiplied by itself. For example, 23 means 2 × 2 × 2 = 8.
What does a negative exponent mean?
A negative exponent means the reciprocal of the base raised to the corresponding positive exponent. For example, 2−3 = 1 / 23 = 0.125.
Can I calculate decimal exponents?
Yes. The Exponent Calculator supports decimal exponents, such as 20.5, which is approximately 1.4142135624.
What does “Use e as base” mean?
When this option is selected, the calculator uses Euler's number, e, approximately 2.718281828, as the base instead of a manually entered base.
Can I use a negative base?
Yes. Negative bases can be used with exponents that produce real-number results. Some fractional exponents with negative bases may produce an invalid real-number result.
Disclaimer
This calculator is provided for general mathematical and educational purposes. While we aim to provide accurate results, SmartMyTools does not guarantee that the results are suitable for professional, academic, financial, engineering, or other specialized applications.